DP Mathematics HL Questionbank

• Syllabus

3.2

Sub sections and their related questions

Definition of $\cos \theta$ , $\sin \theta$ and $\tan \theta$ in terms of the unit circle.

• 12M.1.hl.TZ1.5a: For what values of x does $f(x)$ not exist?
• 12M.1.hl.TZ1.10a: Show that cos $\hat A - \sin \hat A = \frac{1}{{\sqrt 2 }}$.
• 12M.1.hl.TZ2.10a: State the two zeros of f .
• 12M.2.hl.TZ2.3a: By drawing a diagram, show why there are two triangles consistent with this information.
• 12M.2.hl.TZ2.3b: Find the possible values of AC .
• 12N.1.hl.TZ0.1: Given that $\frac{\pi }{2} < \alpha  < \pi$ and $\cos \alpha  = - \frac{3}{4}$, find...
• 12N.2.hl.TZ0.12a: If $\alpha$ is the angle between [CD] and the wall, show that...
• 11M.1.hl.TZ2.13a: (i)     Sketch the graphs of $y = \sin x$ and $y = \sin 2x$ , on the same set of axes, for...
• SPNone.1.hl.TZ0.1a: Write down the value of $\sin \theta$ .
• 13M.1.hl.TZ1.10a: Find all values of x for $0.1 \leqslant x \leqslant 1$ such that $\sin (\pi {x^{ - 1}}) = 0$.
• 13M.2.hl.TZ2.13a: Find an expression for $\theta$ in terms of x, where x is the distance of P from the base of...
• 13M.2.hl.TZ2.13b: (i)     Calculate the value of $\theta$ when x = 0. (ii)     Calculate the value of...
• 11N.1.hl.TZ0.8a: Show that $t = \frac{2}{3}(2\cos \theta + \theta )$.
• 12M.1.hl.TZ1.10b: By squaring both sides of the equation in part (a), solve the equation to find the angles in the...
• 12M.1.hl.TZ1.10c: Apply Pythagoras’ theorem in the triangle ABC to find BC, and hence show that...
• 12M.1.hl.TZ1.10d: Hence, or otherwise, calculate the length of the perpendicular from B to [AC].
• 16M.1.hl.TZ2.3a: Show that $\cot \alpha  = \tan \left( {\frac{\pi }{2} - \alpha } \right)$ for...
• 16N.1.hl.TZ0.13a: Find the value of...

Exact values of $\sin$, $\cos$ and $\tan$ of $0$, $\frac{\pi }{6}$, $\frac{\pi }{4}$, $\frac{\pi }{3}$, $\frac{\pi }{2}$ and their multiples.

• 12M.1.hl.TZ2.2: Find the values of x for which the vectors...
• 12M.1.hl.TZ2.10a: State the two zeros of f .
• 12M.1.hl.TZ1.10b: By squaring both sides of the equation in part (a), solve the equation to find the angles in the...
• 13N.1.hl.TZ0.8: (a)     Prove the trigonometric identity \(\sin (x + y)\sin (x - y) = {\sin ^2}x - {\sin...
• 15M.1.hl.TZ2.11c: Let $y = g \circ f(x)$, find an exact value for $\frac{{{\text{d}}y}}{{{\text{d}}x}}$ at the...
• 15N.1.hl.TZ0.8a: Show that $\sin \left( {\theta  + \frac{\pi }{2}} \right) = \cos \theta$.
• 16M.1.hl.TZ2.3a: Show that $\cot \alpha  = \tan \left( {\frac{\pi }{2} - \alpha } \right)$ for...
• 16M.2.hl.TZ2.11a: Find the value of $\alpha$ when $x = 10$.
• 16M.2.hl.TZ2.11b: Show that $\tan \alpha  = \frac{{2x}}{{{x^2} + 35}}$.
• 16N.1.hl.TZ0.13a: Find the value of...

Definition of the reciprocal trigonometric ratios $\sec \theta$ , $\csc \theta$ and $\cot \theta$ .

• 12M.1.hl.TZ2.9: Show that $\frac{{\cos A + \sin A}}{{\cos A - \sin A}} = \sec 2A + \tan 2A$ .
• 16M.1.hl.TZ2.3a: Show that $\cot \alpha  = \tan \left( {\frac{\pi }{2} - \alpha } \right)$ for...
• 16M.2.hl.TZ2.11a: Find the value of $\alpha$ when $x = 10$.
• 16M.2.hl.TZ2.11b: Show that $\tan \alpha  = \frac{{2x}}{{{x^2} + 35}}$.
• 16N.1.hl.TZ0.13a: Find the value of...

Pythagorean identities: ${\cos ^2}\theta + {\sin ^2}\theta = 1$ ; $1 + {\tan ^2}\theta = {\sec ^2}\theta$ ; $1 + {\cot ^2}\theta = {\csc ^2}\theta$ .

• 12M.1.hl.TZ2.9: Show that $\frac{{\cos A + \sin A}}{{\cos A - \sin A}} = \sec 2A + \tan 2A$ .
• 12M.1.hl.TZ1.10b: By squaring both sides of the equation in part (a), solve the equation to find the angles in the...
• 14N.2.hl.TZ0.14a: Show that $\sin (B + C) = \frac{1}{2}$.
• 15M.2.hl.TZ1.12c: Using (a) (ii) and your answer from (b) show that...
• 16M.1.hl.TZ2.3a: Show that $\cot \alpha  = \tan \left( {\frac{\pi }{2} - \alpha } \right)$ for...
• 16M.2.hl.TZ2.11a: Find the value of $\alpha$ when $x = 10$.
• 16M.2.hl.TZ2.11b: Show that $\tan \alpha  = \frac{{2x}}{{{x^2} + 35}}$.
• 16N.1.hl.TZ0.13a: Find the value of...