DP Mathematics SL Questionbank

• Syllabus

3.3

Sub sections and their related questions

The Pythagorean identity \({\cos ^2}\theta + {\sin ^2}\theta = 1\) .

• 08N.1.sl.TZ0.7a: Show that \(f(x) = \sin x\) .
• 08M.1.sl.TZ1.2b: Find an expression for \(\cos 140^\circ \) .
• 12M.1.sl.TZ1.7a: Show that \(f(x)\) can be expressed as \(1 + \sin 2x\) .
• 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.1.sl.TZ1.7c: The graph of g can be obtained from the graph of f under a horizontal stretch of scale factor p...
• 09N.1.sl.TZ0.6: Solve \(\cos 2x - 3\cos x - 3 - {\cos ^2}x = {\sin ^2}x\) , for \(0 \le x \le 2\pi \) .
• 15M.1.sl.TZ1.5a: find the value of \(\cos x;\)
• 16M.1.sl.TZ2.6a: Write \(h(x)\) in the form \(a\sin (bx)\), where \(a,{\text{ }}b \in \mathbb{Z}\).
• 16M.1.sl.TZ2.6b: Hence find the range of \(h\).
• 16N.1.sl.TZ0.2b: Find \(\cos 2\theta \).
• 17M.1.sl.TZ2.7: Solve \({\log _2}(2\sin x) + {\log _2}(\cos x) =  - 1\), for...
• 17N.1.sl.TZ0.6: Let \(f(x) = 15 - {x^2}\), for \(x \in \mathbb{R}\). The following diagram shows part of the...
• 18M.1.sl.TZ1.10a.i: Find an expression for r in terms of θ.
• 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.1.sl.TZ1.10c: Find the values of θ which give the greatest value of the sum.

Double angle identities for sine and cosine.

• 08N.1.sl.TZ0.7b: Let \(\sin x = \frac{2}{3}\) . Show that \(f(2x) = - \frac{{4\sqrt 5 }}{9}\) .
• 08M.1.sl.TZ2.4a: Given that \(\cos A = \frac{1}{3}\) and \(0 \le A \le \frac{\pi }{2}\) , find \(\cos 2A\) .
• 10N.1.sl.TZ0.5a: Show that \(4 - \cos 2\theta + 5\sin \theta = 2{\sin ^2}\theta + 5\sin \theta + 3\) .
• 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.TZ1.4a: Write down the value of \(\tan \theta \) .
• 10M.1.sl.TZ1.4b(i) and (ii): Find the value of (i)     \(\sin 2\theta \) ; (ii)    \(\cos 2\theta \) .
• 10M.1.sl.TZ2.4a: Find \(f\left( {\frac{\pi }{2}} \right)\) .
• 10M.1.sl.TZ2.4b: Find \((g \circ f)\left( {\frac{\pi }{2}} \right)\) .
• 10M.1.sl.TZ2.4c: Given that \((g \circ f)(x)\) can be written as \(\cos (kx)\) , find the value of k,...
• 09N.1.sl.TZ0.6: Solve \(\cos 2x - 3\cos x - 3 - {\cos ^2}x = {\sin ^2}x\) , for \(0 \le x \le 2\pi \) .
• 09M.1.sl.TZ1.8b: Let the area of the rectangle be A. Show that \(A = 18\sin 2\theta \) .
• SPNone.1.sl.TZ0.6a: Find the value of a and of b .
• 11N.1.sl.TZ0.6a: Find \(\cos \theta \) .
• 11N.1.sl.TZ0.6b: Find \(\tan 2\theta \) .
• 11M.2.sl.TZ2.10a: Show that the area of the window is given by \(y = 4\sin \theta + 2\sin 2\theta \) .
• 11M.2.sl.TZ2.10b: Zoe wants a window to have an area of \(5{\text{ }}{{\text{m}}^2}\). Find the two possible values...
• 11M.2.sl.TZ2.10c: John wants two windows which have the same area A but different values of \(\theta \) . Find all...
• 14M.1.sl.TZ2.1b: Find \(\cos 2A\).
• 15M.1.sl.TZ1.5b: find the value of \(\cos 2x.\)
• 16M.1.sl.TZ2.6a: Write \(h(x)\) in the form \(a\sin (bx)\), where \(a,{\text{ }}b \in \mathbb{Z}\).
• 16M.1.sl.TZ2.6b: Hence find the range of \(h\).
• 16N.1.sl.TZ0.2b: Find \(\cos 2\theta \).
• 17M.1.sl.TZ2.7: Solve \({\log _2}(2\sin x) + {\log _2}(\cos x) =  - 1\), for...
• 17N.1.sl.TZ0.6: Let \(f(x) = 15 - {x^2}\), for \(x \in \mathbb{R}\). The following diagram shows part of the...
• 18M.1.sl.TZ1.6: Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.This is...
• 18M.1.sl.TZ1.10a.i: Find an expression for r in terms of θ.
• 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.1.sl.TZ1.10c: Find the values of θ which give the greatest value of the sum.

Relationship between trigonometric ratios.

• 12N.1.sl.TZ0.5a: Let \(\sin {100^ \circ } = m\). Find an expression for \(\cos {100^ \circ }\) in terms of m.
• 12N.1.sl.TZ0.5b: Let \(\sin {100^ \circ } = m\) . Find an expression for \(\tan {100^ \circ }\) in terms of m.
• 12N.1.sl.TZ0.5c: Let \(\sin {100^ \circ } = m\). Find an expression for \(\sin {200^ \circ }\) in terms of m.
• 08N.1.sl.TZ0.7b: Let \(\sin x = \frac{2}{3}\) . Show that \(f(2x) = - \frac{{4\sqrt 5 }}{9}\) .
• 08M.1.sl.TZ2.4b: Given that \(\sin B = \frac{2}{3}\)  and \(\frac{\pi }{2} \le B \le \pi \) , find \(\cos B\) .
• 12M.1.sl.TZ1.7a: Show that \(f(x)\) can be expressed as \(1 + \sin 2x\) .
• 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.1.sl.TZ1.7c: The graph of g can be obtained from the graph of f under a horizontal stretch of scale factor p...
• 09M.1.sl.TZ1.9c: (i)     Find \({\rm{sinR}}\widehat {\rm{P}}{\rm{Q}}\) . (ii)    Hence, find the area of triangle...
• 11N.1.sl.TZ0.6a: Find \(\cos \theta \) .
• 11N.1.sl.TZ0.6b: Find \(\tan 2\theta \) .
• 14M.1.sl.TZ2.1a: Show that \(\cos A = \frac{{12}}{{13}}\).
• 18M.1.sl.TZ1.6: Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.This is...