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Topic 3 - Circular functions and trigonometry

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Topic 3 - Circular functions and trigonometry

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The aims of this topic are to explore the circular functions and to solve problems using trigonometry. On examination papers, radian measure should be assumed unless otherwise indicated.

Directly related questions

12N.1.sl.TZ0.5c: Let \(\sin {100^ \circ } = m\). Find an expression for \(\sin {200^ \circ }\) in terms of m.
12N.2.sl.TZ0.5a(i) and (ii): Write down the value of (i) \(a\) ; (ii) \(c\) .
12M.2.sl.TZ2.1a: Find \({\rm{R\hat PQ}}\) .
12M.2.sl.TZ2.10a: Use the cosine rule to show that \({\rm{PQ}} = 2r\sin \theta \) .
12M.2.sl.TZ2.10c(i) and (ii): Consider the function \(f(\theta ) = 2.6\sin \theta - 2\theta \) , for...
12M.2.sl.TZ2.10b: Let l be the length of the arc PRQ . Given that \(1.3{\rm{PQ}} - l = 0\) , find the value of...
08N.1.sl.TZ0.7b: Let \(\sin x = \frac{2}{3}\) . Show that \(f(2x) = - \frac{{4\sqrt 5 }}{9}\) .
08N.1.sl.TZ0.10b: The transformation P is given by a horizontal stretch of a scale factor of \(\frac{1}{2}\) ,...
08N.2.sl.TZ0.8d: Hence, or otherwise, find the area of the parallelogram.
08M.1.sl.TZ1.2b: Find an expression for \(\cos 140^\circ \) .
08M.1.sl.TZ1.4b: On the diagram below, sketch the curve of g, for \(0 \le x \le 2\pi \) .
08M.2.sl.TZ1.2b: Find the area of triangle PQR.
08M.2.sl.TZ1.3c: Find the area of sector OABC.
12M.2.sl.TZ1.9c: Find \({\rm{A}}\widehat {\rm{D}}{\rm{B}}\) .
12M.2.sl.TZ1.9d(i) and (ii): (i) Show that \({\rm{C}}\widehat {\rm{B}}{\rm{D}} = 1.29\) radians, correct to 2 decimal...
10M.1.sl.TZ1.9a: Use the quotient rule to show that \(f'(x) = \frac{{ - 1}}{{{{\sin }^2}x}}\) .
10M.1.sl.TZ2.10a(i) and (ii): Solve for \(0 \le x < 2\pi \) (i) \(6 + 6\sin x = 6\) ; (ii) \(6 + 6\sin x = 0\) .
09N.2.sl.TZ0.8d: Find the area of region ABCD.
10N.2.sl.TZ0.10b: After six minutes, the seat is at point Q. Find its height above the ground at Q.
10M.2.sl.TZ2.8d: Find EF .
SPNone.2.sl.TZ0.6: Find the height of the building.
SPNone.2.sl.TZ0.7a: Find an expression for the area of the shaded region.
11N.1.sl.TZ0.9b: Show that \(b = \frac{\pi }{4}\) .
11N.2.sl.TZ0.4b: Hence, find \({\rm{A}}\widehat {\rm{B}}{\rm{C}}\) , given that it is acute.
11N.2.sl.TZ0.3a: Find the value of \(\theta \) .
11M.2.sl.TZ1.1a: Find AC .
11M.1.sl.TZ2.10c: Sketch the graph of h , for \(0 \le t \le 40\) .
14M.2.sl.TZ1.1b: Find \({\rm{B\hat CA}}\).
14M.2.sl.TZ2.6b(i): Find \(p\).
14M.2.sl.TZ2.6c: Solve \(f(x) = 7\).
13M.1.sl.TZ2.5c: \(r\) .
15N.2.sl.TZ0.8a: Find \(AC\).
15N.2.sl.TZ0.1a: Find the length of arc \(ABC\).
15N.2.sl.TZ0.1b: Find the area of the shaded region.
16M.1.sl.TZ1.3a: (i) Write down the amplitude of \(f\). (ii) Find the period of \(f\).
16M.2.sl.TZ2.4c: Calculate the time needed for the seat to complete a full rotation, giving your answer correct to...
17M.1.sl.TZ2.7: Solve \({\log _2}(2\sin x) + {\log _2}(\cos x) = - 1\), for...
17M.1.sl.TZ2.9b.ii: Find \(\left| {\overrightarrow {{\text{AB}}} } \right|\).
17M.2.sl.TZ1.8a.ii: Find the difference in height between low tide and high tide.
17M.2.sl.TZ1.8c: There are two high tides on 12 December 2017. At what time does the second high tide occur?
17N.2.sl.TZ0.1a: Find BC.
18M.2.sl.TZ2.6a: After 8 minutes, the seat is 117 m above the ground. Find k.
18M.2.sl.TZ2.6b: Find the value of a.
18M.2.sl.TZ2.8d: Hence or otherwise find the shortest distance from R to the line through P and Q.
12N.1.sl.TZ0.5a: Let \(\sin {100^ \circ } = m\). Find an expression for \(\cos {100^ \circ }\) in terms of m.
12N.2.sl.TZ0.5b: Find the value of b .
12N.2.sl.TZ0.5c: Find the x-coordinate of R.
12N.2.sl.TZ0.8b: Find the area of triangle AOB.
12M.2.sl.TZ2.1c: Find the area of \(\Delta {\rm{PQR}}\) .
12M.2.sl.TZ2.1b: Find PR .
08M.2.sl.TZ1.3a: Find the value of r.
12M.1.sl.TZ1.7b: The graph of f is shown below for \(0 \le x \le 2\pi \) . Let \(g(x) = 1 + \cos x\) . On the...
12M.2.sl.TZ1.9b: Write down the length of BD.
10M.1.sl.TZ2.4a: Find \(f\left( {\frac{\pi }{2}} \right)\) .
10M.1.sl.TZ2.10b: Write down the exact value of the x-intercept of f , for \(0 \le x < 2\pi \) .
10M.1.sl.TZ2.10c: The area of the shaded region is k . Find the value of k , giving your answer in terms of \(\pi \) .
10M.1.sl.TZ2.10d: Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . The graph of f is transformed to...
09M.2.sl.TZ1.2b: Find the area of the shaded region.
09M.1.sl.TZ2.7: Let \(f(x) = \sqrt 3 {{\rm{e}}^{2x}}\sin x + {{\rm{e}}^{2x}}\cos x\) , for \(0 \le x \le \pi \) ....
10N.2.sl.TZ0.6a: Find \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .
10N.2.sl.TZ0.6b: Find AB.
10M.2.sl.TZ1.5b: The equation \(y = k\) has exactly two solutions. Write down the value of k.
11N.1.sl.TZ0.6b: Find \(\tan 2\theta \) .
11N.1.sl.TZ0.9d: At a point R, the gradient is \( - 2\pi \) . Find the x-coordinate of R.
14M.2.sl.TZ1.1a: Find AC.
14M.2.sl.TZ2.1a(i): Find the length of the arc \({\text{ABC}}\).
14M.2.sl.TZ2.5a: Find the two possible values for \(\hat A\).
13M.1.sl.TZ2.5b: \(q\)
15N.2.sl.TZ0.8c: The area of triangle \(ACD\) is half the area of triangle \(ABC\). Find the possible values of...
09M.2.sl.TZ2.10e: Write down the two values of k for which the equation \(f(x) = k\) has exactly two solutions.
14M.1.sl.TZ1.6: Let \(\int_\pi ^a {\cos 2x{\text{d}}x} = \frac{1}{2}{\text{, where }}\pi < a < 2\pi \)....
15M.1.sl.TZ1.2a: Find the length of \({\text{arc ACB}}\).
15M.1.sl.TZ1.5a: find the value of \(\cos x;\)
16M.1.sl.TZ1.3b: On the following grid sketch the graph of \(f\).
17M.2.sl.TZ1.8b.ii: Find the value of \(q\);
17N.1.sl.TZ0.6: Let \(f(x) = 15 - {x^2}\), for \(x \in \mathbb{R}\). The following diagram shows part of the...
17N.2.sl.TZ0.1b: Find the area of triangle ABC.
17N.2.sl.TZ0.10a: Show that \(f(2\pi ) = 2\pi \).
17N.2.sl.TZ0.10c: Show that the distance between the \(x\)-coordinates of \({{\text{P}}_k}\) and...
18M.2.sl.TZ1.10b.i: For the graph of \(f\), write down the amplitude.
18M.2.sl.TZ1.10d: Find the maximum speed of the ball.
18M.2.sl.TZ2.2b: Find DC.
08N.1.sl.TZ0.10c: The graph of g is the image of the graph of f under P. Find \(g(t)\) in the form...
08N.2.sl.TZ0.6a: Find the distance the second ship will travel.
08M.2.sl.TZ1.3b: Find the perimeter of sector OABC.
08M.1.sl.TZ2.4a: Given that \(\cos A = \frac{1}{3}\) and \(0 \le A \le \frac{\pi }{2}\) , find \(\cos 2A\) .
08M.1.sl.TZ2.10a: Find the area of the triangle OPB, in terms of \(\theta \) .
12M.1.sl.TZ1.7c: The graph of g can be obtained from the graph of f under a horizontal stretch of scale factor p...
10M.1.sl.TZ1.9b: Find \(f''(x)\) .
09N.2.sl.TZ0.9b: Consider the graph of \(f\) . Write down (i) the x-intercept that lies between \(x = 0\) and...
09M.2.sl.TZ1.3b: Write down the period of \(h\) .
10N.2.sl.TZ0.10c: The height of the seat above ground after t minutes can be modelled by the function...
10M.2.sl.TZ2.8b: Hence find the area of the shaded region.
SPNone.1.sl.TZ0.6b: Hence or otherwise, solve the equation \(6\sin x\cos x = \frac{3}{2}\) , for...
11N.2.sl.TZ0.4a: Find the two possible values of \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .
11M.1.sl.TZ2.10a(i) and (ii): Write down the height of P above ground level after (i) 10 minutes; (ii) 15 minutes.
11M.1.sl.TZ2.10b(i) and (ii): (i) Show that \(h(8) = 90.5\). (ii) Find \(h(21)\) .
11M.2.sl.TZ2.10b: Zoe wants a window to have an area of \(5{\text{ }}{{\text{m}}^2}\). Find the two possible values...
13M.2.sl.TZ2.3a: Find \(x\) .
13M.2.sl.TZ2.3b: Find BC.
14M.2.sl.TZ1.5a: Find the number of deer in the reserve on 1 May 2014.
14M.1.sl.TZ2.1b: Find \(\cos 2A\).
14M.2.sl.TZ2.6b(ii): Find \(q\).
13N.1.sl.TZ0.5a: Find the value of \(k\).
13N.1.sl.TZ0.5b: Find the minimum value of \(f(x)\).
13M.1.sl.TZ2.5a: \(p\)
13M.2.sl.TZ1.8c: Find the area of triangle ADC.
14N.2.sl.TZ0.5c: \(q\).
15M.1.sl.TZ1.2b: Find the perimeter of the shaded region.
16N.2.sl.TZ0.3b: Find the value of \(r\).
16N.1.sl.TZ0.2a: Find \(\cos \theta \).
16M.2.sl.TZ2.2a: Find BD.
16N.1.sl.TZ0.8c: Write down an expression in terms of \(\theta \) for (i) angle ADB; (ii) area of...
17M.2.sl.TZ1.8a.i: How much time is there between the first low tide and the next high tide?
17N.2.sl.TZ0.10b.ii: Find the equation of \(L\).
18M.1.sl.TZ1.10a.i: Find an expression for r in terms of θ.
18M.2.sl.TZ2.2a: Find DB.
08N.1.sl.TZ0.7a: Show that \(f(x) = \sin x\) .
12M.2.sl.TZ1.9a(i) and (ii): (i) Show that \({p^2}(41 - 40\cos 0.7) = 36\) . (ii) Find p .
10M.1.sl.TZ1.4a: Write down the value of \(\tan \theta \) .
10M.1.sl.TZ1.9d: Use information from the table to explain why there is a point of inflexion on the graph of f...
09M.1.sl.TZ2.8b: Let \(h(x) = {{\rm{e}}^{ - 3x}}\sin \left( {x - \frac{\pi }{3}} \right)\) . Find the exact value...
10N.2.sl.TZ0.10a: Find the height of a seat above the ground after 15 minutes.
13M.2.sl.TZ1.10a: Find the maximum height above the ground of the seat.
13M.2.sl.TZ1.8d: Hence or otherwise, find the total area of the shaded regions.
13M.2.sl.TZ1.10b: (i) Show that the period of \(h\) is \(25\) minutes. (ii) Write down the exact value of...
14N.2.sl.TZ0.3b: Find \(AB\).
15N.1.sl.TZ0.4c: On the following grid, sketch the graph of \(y = f(x)\), for \(0 \le x \le 3\).
15N.2.sl.TZ0.8d: Given that \(\theta \) is obtuse, find \(CD\).
16M.2.sl.TZ1.3c: Use the sine rule to find \({\rm{A\hat CB}}\).
16M.1.sl.TZ2.5b: Find the exact area of the sector BDC.
16M.2.sl.TZ2.4a: Find the height of the seat when \(t = 0\).
16N.1.sl.TZ0.2b: Find \(\cos 2\theta \).
17M.2.sl.TZ1.8b.i: Find the value of \(p\);
17N.1.sl.TZ0.4a: Show that \({\text{AC}} = 7{\text{ cm}}\).
17N.2.sl.TZ0.10b.i: Find the coordinates of \({{\text{P}}_0}\) and of \({{\text{P}}_1}\).
18M.1.sl.TZ1.6: Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.This is...
18M.2.sl.TZ1.3b: The area of the shaded region is 12 cm2. Find the value of θ.
18M.2.sl.TZ1.10a: Find the coordinates of A.
18M.2.sl.TZ1.10b.ii: For the graph of \(f\), write down the period.
08M.1.sl.TZ1.4c: Write down the number of solutions to the equation \(g(x) = 2\) , for \(0 \le x \le 2\pi \) .
08M.1.sl.TZ2.9a: (i) Write down the range of the function f . (ii) Consider \(f(x) = 1\) , \(0 \le x \le 2\pi \)...
08M.2.sl.TZ2.8a(i), (ii) and (iii): Use the graph to write down an estimate of the value of t when (i) the depth of water is...
08M.2.sl.TZ2.8b(i), (ii) and (iii): The depth of water can be modelled by the function \(y = \cos A(B(t - 1)) + C\) . (i) Show...
12M.1.sl.TZ1.5b(i) and (ii): (i) Show that the period of f is \(\pi \) . (ii) Hence, find the value of b .
10N.1.sl.TZ0.5a: Show that \(4 - \cos 2\theta + 5\sin \theta = 2{\sin ^2}\theta + 5\sin \theta + 3\) .
09N.2.sl.TZ0.8b: Find OD.
09M.2.sl.TZ1.2a: Find AB.
09M.2.sl.TZ2.4a: Find the size of angle ACB.
09M.2.sl.TZ2.4b: Find the size of angle CAD.
09M.2.sl.TZ2.10c: Hence write \(f(x)\) in the form \(p\sin (qx + r)\) .
10M.2.sl.TZ1.5a(i), (ii) and (iii): Find the value of (i) p ; (ii) q ; (iii) r.
10M.2.sl.TZ1.8a: Use the cosine rule to show that \({\rm{AC}} = \sqrt {41 - 40\cos x} \) .
10M.2.sl.TZ1.8d(i) and (ii): (i) Find y. (ii) Hence, or otherwise, find the area of triangle ACD.
10N.2.sl.TZ0.10d: The height of the seat above ground after t minutes can be modelled by the function...
11N.1.sl.TZ0.9c: Find \(f'(x)\) .
11N.2.sl.TZ0.3b: Find the area of the shaded region.
13M.2.sl.TZ1.8a: Find AC.
13M.2.sl.TZ1.10d: Sketch the graph of \(h\) , for \(0 \le t \le 50\) .
14N.1.sl.TZ0.7: The following diagram shows triangle \(ABC\). Let...
11M.2.sl.TZ1.8c: In the first rotation, there are two values of t when the bucket is descending at a rate of...
15M.2.sl.TZ2.1a: Find \(AC\).
16M.2.sl.TZ1.3a: Find \({\rm{A\hat BC}}\).
16M.1.sl.TZ2.6a: Write \(h(x)\) in the form \(a\sin (bx)\), where \(a,{\text{ }}b \in \mathbb{Z}\).
16M.2.sl.TZ2.4b: The seat first reaches a height of 20 m after \(k\) minutes. Find \(k\).
16N.2.sl.TZ0.10a: (i) Find the value of \(c\). (ii) Show that \(b = \frac{\pi }{6}\). (iii) Find the...
16N.2.sl.TZ0.10b: (i) Write down the value of \(k\). (ii) Find \(g(x)\).
16N.2.sl.TZ0.10c: (i) Find \(w\). (ii) Hence or otherwise, find the maximum positive rate of change of \(g\).
17M.1.sl.TZ2.9c: Find \(\cos {\rm{B\hat AC}}\).
17M.2.sl.TZ2.1b: Find the perimeter of sector OABC.
17M.2.sl.TZ2.9b: Finds CE.
17M.2.sl.TZ2.9c: Find DE.
17M.2.sl.TZ2.9d: When the ship reaches D, it changes direction and travels directly to the island at 50 km per...
17N.2.sl.TZ0.10d: A saw has a toothed edge which is 300 mm long. Find the number of complete teeth on this saw.
18M.1.sl.TZ1.10a.ii: Find the possible values of r.
18M.1.sl.TZ1.10b: Show that the sum of the infinite sequence...
18M.2.sl.TZ1.3a: Find the area of the shaded region, in terms of θ.
18M.2.sl.TZ1.6: Triangle ABC has a = 8.1 cm, b = 12.3 cm and area 15 cm2. Find the largest possible perimeter of...
18M.2.sl.TZ2.8b: Find the angle between PQ and PR.
12N.2.sl.TZ0.8e: Angle BOC is 2.4 radians. The shaded region is to be painted red. Red paint is sold in cans...
12M.1.sl.TZ2.3c: Write down the equation of the normal to the curve at P.
08N.1.sl.TZ0.10a(i), (ii), (iii) and (iv): (i) Find the value of a. (ii) Show that \(b = \frac{\pi }{6}\) . (iii) Find the value...
08N.2.sl.TZ0.6b: Find the bearing of the course taken by the second ship.
08M.1.sl.TZ1.4a: Write down the period of g.
08M.2.sl.TZ1.2a: Find \({\rm{P}}\widehat {\rm{R}}{\rm{Q}}\) .
08M.1.sl.TZ2.4b: Given that \(\sin B = \frac{2}{3}\) and \(\frac{\pi }{2} \le B \le \pi \) , find \(\cos B\) .
08M.1.sl.TZ2.10b: Explain why the area of triangle OPA is the same as the area triangle OPB.
12M.1.sl.TZ1.5a: Find the value of a .
12M.1.sl.TZ1.5c: Given that \(0 < c < \pi \) , write down the value of c .
10N.1.sl.TZ0.3b: Find the area of the shaded region.
10M.1.sl.TZ1.9c: Find the value of p and of q.
10M.2.sl.TZ1.8c: (i) Hence, find x, giving your answer to two decimal places. (ii) Find AC .
SPNone.1.sl.TZ0.10d: The function \(f(x)\) can be written in the form \(r\cos (x - a)\) . Write down the value of r...
SPNone.2.sl.TZ0.7b: The chord [AB] divides the area of the circle in the ratio 1:7. Find the value of \(\theta \) .
11M.1.sl.TZ1.6: Solve the equation \(2\cos x = \sin 2x\) , for \(0 \le x \le 3\pi \) .
11M.2.sl.TZ1.8d: In the first rotation, there are two values of t when the bucket is descending at a rate of...
11M.2.sl.TZ2.10a: Show that the area of the window is given by \(y = 4\sin \theta + 2\sin 2\theta \) .
13M.2.sl.TZ2.7b: The area of the shaded region is \(25\) cm2 . Find the value of \(r\) .
14M.2.sl.TZ1.9c(i): The function \(f\) can also be written in the form...
14M.2.sl.TZ2.1a(ii): Find the perimeter of the shaded sector.
14M.2.sl.TZ2.1b: Find the area of the shaded sector.
14M.2.sl.TZ2.5b: Given that \(\hat A\) is obtuse, find \({\text{BC}}\).
13N.1.sl.TZ0.5c: Let \(g(x) = \sin x\). The graph of g is translated to the graph of \(f\) by the...
14N.2.sl.TZ0.5b: \(r\);
14N.2.sl.TZ0.5a: \(p\);
15N.2.sl.TZ0.8b: Find the area of triangle \(ABC\).
10N.1.sl.TZ0.3a: Find the length of the arc ACB .
10M.1.sl.TZ2.4b: Find \((g \circ f)\left( {\frac{\pi }{2}} \right)\) .
15M.2.sl.TZ2.10b: When \(\theta = \alpha \), the area of the square \(ABCD\) is equal to the area of the sector...
16M.1.sl.TZ2.5a: Find \({\rm{A\hat BC}}\).
16M.1.sl.TZ2.6b: Hence find the range of \(h\).
17M.1.sl.TZ2.9a: Find the coordinates of A.
17M.1.sl.TZ2.9d: Hence or otherwise, find the distance between \({P_1}\) and \({P_2}\) two seconds after they...
17M.2.sl.TZ1.5: The following diagram shows the chord [AB] in a circle of radius 8 cm, where...
17M.2.sl.TZ2.4a: Find the value of \(p\).
17M.2.sl.TZ2.4c: Use the model to find the depth of the water 10 hours after high tide.
18M.2.sl.TZ1.10c: Hence, write \(f\left( x \right)\) in the form \(p\,\,{\text{cos}}\,\left( {x + r} \right)\).
18M.2.sl.TZ1.10e: Find the first time when the ball’s speed is changing at a rate of 2 cm s−2.
18M.2.sl.TZ2.8c: Find the area of triangle PQR.
12M.1.sl.TZ2.3b: Write down the gradient of the curve at P.
12M.2.sl.TZ2.10d: Use the graph of f to find the values of \(\theta \) for which \(l < 1.3{\rm{PQ}}\) .
08M.1.sl.TZ1.2a(i) and (ii): Write down an expression for (i) \(\sin 140^\circ \) ; (ii) \(\cos 70^\circ \) .
08M.2.sl.TZ2.8c: A sailor knows that he cannot sail past P when the depth of the water is less than 12 m ....
10N.1.sl.TZ0.5b: Hence, solve the equation \(4 - \cos 2\theta + 5\sin \theta = 0\) for \(0 \le \theta \le 2\pi \) .
10M.1.sl.TZ2.4c: Given that \((g \circ f)(x)\) can be written as \(\cos (kx)\) , find the value of k,...
09N.2.sl.TZ0.8a: Find AD.
09N.2.sl.TZ0.8c: Find the area of sector OABC.
09M.1.sl.TZ1.8a: Write down an expression in terms of \(\theta \) for (i) \(x\) ; (ii) \(y\) .
09M.1.sl.TZ1.9c: (i) Find \({\rm{sinR}}\widehat {\rm{P}}{\rm{Q}}\) . (ii) Hence, find the area of triangle...
09M.2.sl.TZ1.3c: Write down the range of \(h\) .
10M.2.sl.TZ1.8b: Use the sine rule in triangle ABC to find another expression for AC.
10M.2.sl.TZ2.8a: Find the size of angle AOC .
11N.1.sl.TZ0.6a: Find \(\cos \theta \) .
11N.1.sl.TZ0.9a(i), (ii) and (iii): Use the graph to write down the value of (i) a ; (ii) c ; (iii) d .
11M.2.sl.TZ1.1b: Find \({\rm{B}}\widehat {\rm{A}}{\rm{C}}\) .
11M.2.sl.TZ1.8a: Show that \(a = 4\) .
11M.1.sl.TZ2.10d: Given that h can be expressed in the form \(h(t) = a\cos bt + c\) , find a , b and c .
11M.2.sl.TZ2.5b: Find x .
14M.1.sl.TZ2.1a: Show that \(\cos A = \frac{{12}}{{13}}\).
13N.2.sl.TZ0.8a: Find \({\rm{B\hat AC}}\).
13N.2.sl.TZ0.8b: Find \({\text{AC}}\).
13N.2.sl.TZ0.8c: Hence or otherwise, find the length of arc \({\text{ABC}}\).
13M.2.sl.TZ1.10c: Find the value of \(a\) .
14N.2.sl.TZ0.3a: Find the length of arc \(ACB\).
15N.1.sl.TZ0.4b: Find the period of \(f\).
13M.2.sl.TZ1.10e: In one rotation of the wheel, find the probability that a randomly selected seat is at least...
16N.2.sl.TZ0.3a: Write down the exact value of \(\theta \) in radians.
16N.2.sl.TZ0.3c: Find AB.
16M.2.sl.TZ1.3b: Find the distance from Town A to Town C.
17M.1.sl.TZ1.10c: Let \(y = \frac{1}{{\cos x}}\), for \(0 < x < \frac{\pi }{2}\). The graph of \(y\)between...
17M.2.sl.TZ1.8b.iii: Find the value of \(r\).
17N.1.sl.TZ0.4b: The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the...
18M.1.sl.TZ1.10c: Find the values of θ which give the greatest value of the sum.
18M.2.sl.TZ2.6c: Find when the seat is 30 m above the ground for the third time.
12N.1.sl.TZ0.5b: Let \(\sin {100^ \circ } = m\) . Find an expression for \(\tan {100^ \circ }\) in terms of m.
12N.2.sl.TZ0.8a: Find the length of the chord [AB].
12N.2.sl.TZ0.8c: Angle BOC is 2.4 radians. Find the length of arc ADC.
12N.2.sl.TZ0.8d: Angle BOC is 2.4 radians. Find the area of the shaded region.
12M.1.sl.TZ2.3a(i) and (ii): (i) Write down the value of a . (ii) Find the value of b .
08N.1.sl.TZ0.10d: The graph of g is the image of the graph of f under P. Give a full geometric description of the...
08M.1.sl.TZ1.2c: Find an expression for \(\tan 140^\circ \) .
12M.1.sl.TZ1.7a: Show that \(f(x)\) can be expressed as \(1 + \sin 2x\) .
10M.1.sl.TZ1.4b(i) and (ii): Find the value of (i) \(\sin 2\theta \) ; (ii) \(\cos 2\theta \) .
10M.1.sl.TZ2.10e: Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . The graph of f is transformed to...
09N.1.sl.TZ0.6: Solve \(\cos 2x - 3\cos x - 3 - {\cos ^2}x = {\sin ^2}x\) , for \(0 \le x \le 2\pi \) .
10M.2.sl.TZ2.8c: The area of sector OCDE is \(45{\text{ c}}{{\text{m}}^2}\). Find the size of angle COE .
SPNone.1.sl.TZ0.6a: Find the value of a and of b .
SPNone.1.sl.TZ0.10c: Find the maximum value of \(f(x)\) .
11M.2.sl.TZ1.8b: The wheel turns at a rate of one rotation every 30 seconds. Show that \(b = \frac{\pi }{{15}}\) .
11M.1.sl.TZ2.4: Let \(h(x) = \frac{{6x}}{{\cos x}}\) . Find \(h'(0)\) .
11M.2.sl.TZ2.5a: Complete the diagram, showing clearly all the information above.
11M.2.sl.TZ2.10c: John wants two windows which have the same area A but different values of \(\theta \) . Find all...
13M.2.sl.TZ1.8b: (i) Find \(A\hat CD\) . (ii) Hence, find \(A\hat CB\) .
09M.1.sl.TZ1.8b: Let the area of the rectangle be A. Show that \(A = 18\sin 2\theta \) .
14M.2.sl.TZ1.9c(ii): The function \(f\) can also be written in the form...
14M.2.sl.TZ2.6a: Write down the value of \(r\).
15N.1.sl.TZ0.4a: Write down the amplitude of \(f\).
15M.1.sl.TZ1.5b: find the value of \(\cos 2x.\)
15M.2.sl.TZ2.1b: Find the area of triangle \(ABC\).
15M.2.sl.TZ2.10a: Show that the area of the square \(ABCD\) is \(2{r^2}(1 - \cos \theta )\).
16M.2.sl.TZ2.2b: Find \({\rm{D\hat BC}}\).
17M.1.sl.TZ1.3: The following diagram shows triangle PQR. Find PR.
17M.1.sl.TZ1.10a: Show that \(\cos \theta = \frac{3}{4}\).
17M.1.sl.TZ1.10b: Given that \(\tan \theta > 0\), find \(\tan \theta \).
17M.1.sl.TZ2.9b.i: Find \(\overrightarrow {{\text{AB}}} \);
17M.2.sl.TZ2.1a: Find the length of arc ABC.
17M.2.sl.TZ2.1c: Find the area of sector OABC.
17M.2.sl.TZ2.4b: Find the value of \(q\).
17M.2.sl.TZ2.9a: Find the bearing of A from E.
18M.1.sl.TZ2.4: The following diagram shows a circle with centre O and radius r cm. The points A and B lie on...
18M.2.sl.TZ2.8a.i: Find \(\mathop {{\text{PQ}}}\limits^ \to \).
18M.2.sl.TZ2.8a.ii: Find \(\left| {\mathop {{\text{PQ}}}\limits^ \to } \right|\).

Sub sections and their related questions

DP Mathematics SL Questionbank

Topic 3 - Circular functions and trigonometry

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Directly related questions

Sub sections and their related questions

3.1

3.2

3.3

3.4

3.5

3.6