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...