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The circular functions \(\sin x\) , \(\cos x\) and \(\tan x\) : their domains and ranges; amplitude, their periodic nature; and their graphs.

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Topic 3 - Circular functions and trigonometry » 3.4 » The circular functions \(\sin x\) , \(\cos x\) and \(\tan x\) : their domains and ranges; amplitude, their periodic nature; and their graphs.

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Directly related questions

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.
17N.2.sl.TZ0.10c: Show that the distance between the \(x\)-coordinates of \({{\text{P}}_k}\) and...
17N.2.sl.TZ0.10b.ii: Find the equation of \(L\).
17N.2.sl.TZ0.10b.i: Find the coordinates of \({{\text{P}}_0}\) and of \({{\text{P}}_1}\).
17N.2.sl.TZ0.10a: Show that \(f(2\pi ) = 2\pi \).
17M.2.sl.TZ1.8c: There are two high tides on 12 December 2017. At what time does the second high tide occur?
17M.2.sl.TZ1.8b.iii: Find the value of \(r\).
17M.2.sl.TZ1.8b.ii: Find the value of \(q\);
17M.2.sl.TZ1.8b.i: Find the value of \(p\);
17M.2.sl.TZ1.8a.ii: Find the difference in height between low tide and high tide.
17M.2.sl.TZ1.8a.i: How much time is there between the first low tide and the next high tide?
18M.2.sl.TZ2.6c: Find when the seat is 30 m above the ground for the third time.
18M.2.sl.TZ2.6b: Find the value of a.
18M.2.sl.TZ2.6a: After 8 minutes, the seat is 117 m above the ground. Find k.
18M.2.sl.TZ1.10b.ii: For the graph of \(f\), write down the period.
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.TZ1.10d: Find the maximum speed of the ball.
18M.2.sl.TZ1.10c: Hence, write \(f\left( x \right)\) in the form \(p\,\,{\text{cos}}\,\left( {x + r} \right)\).
18M.2.sl.TZ1.10b.i: For the graph of \(f\), write down the amplitude.
18M.2.sl.TZ1.10a: Find the coordinates of A.
16M.1.sl.TZ2.6b: Hence find the range of \(h\).
16M.1.sl.TZ2.6a: Write \(h(x)\) in the form \(a\sin (bx)\), where \(a,{\text{ }}b \in \mathbb{Z}\).
16M.1.sl.TZ1.3b: On the following grid sketch the graph of \(f\).
16M.1.sl.TZ1.3a: (i) Write down the amplitude of \(f\). (ii) Find the period of \(f\).
16N.2.sl.TZ0.10b: (i) Write down the value of \(k\). (ii) Find \(g(x)\).
16N.2.sl.TZ0.10a: (i) Find the value of \(c\). (ii) Show that \(b = \frac{\pi }{6}\). (iii) Find the...
12N.2.sl.TZ0.5a(i) and (ii): Write down the value of (i) \(a\) ; (ii) \(c\) .
12N.2.sl.TZ0.5b: Find the value of b .
12N.2.sl.TZ0.5c: Find the x-coordinate of R.
12M.1.sl.TZ2.3a(i) and (ii): (i) Write down the value of a . (ii) Find the value of b .
12M.1.sl.TZ2.3b: Write down the gradient of the curve at P.
12M.1.sl.TZ2.3c: Write down the equation of the normal to the curve at P.
08M.1.sl.TZ1.4a: Write down the period of g.
08M.1.sl.TZ1.4b: On the diagram below, sketch the curve of g, for \(0 \le x \le 2\pi \) .
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...
12M.1.sl.TZ1.5a: Find the value of a .
12M.1.sl.TZ1.5b(i) and (ii): (i) Show that the period of f is \(\pi \) . (ii) Hence, find the value of b .
12M.1.sl.TZ1.5c: Given that \(0 < c < \pi \) , write down the value of c .
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 \(h\) .
09M.2.sl.TZ1.3c: Write down the range of \(h\) .
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.1.sl.TZ2.10c: Sketch the graph of h , for \(0 \le t \le 40\) .
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 .
13M.2.sl.TZ1.10a: Find the maximum height above the ground of the seat.
14M.2.sl.TZ1.5a: Find the number of deer in the reserve on 1 May 2014.
14M.2.sl.TZ1.9c(i): The function \(f\) can also be written in the form...
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 \(r\).
14M.2.sl.TZ2.6b(i): Find \(p\).
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 \(f(x)\).
13N.1.sl.TZ0.5c: Let \(g(x) = \sin x\). The graph of g is translated to the graph of \(f\) by the...
13M.1.sl.TZ2.5a: \(p\)
13M.1.sl.TZ2.5c: \(r\) .
13M.1.sl.TZ2.5b: \(q\)
13M.2.sl.TZ1.10c: Find the value of \(a\) .
13M.2.sl.TZ1.10b: (i) Show that the period of \(h\) is \(25\) minutes. (ii) Write down the exact value of...
13M.2.sl.TZ1.10d: Sketch the graph of \(h\) , for \(0 \le t \le 50\) .
14N.2.sl.TZ0.5b: \(r\);
14N.2.sl.TZ0.5a: \(p\);
14N.2.sl.TZ0.5c: \(q\).
15N.1.sl.TZ0.4a: Write down the amplitude of \(f\).
15N.1.sl.TZ0.4b: Find the period of \(f\).
15N.1.sl.TZ0.4c: On the following grid, sketch the graph of \(y = f(x)\), for \(0 \le x \le 3\).

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