# Trigonometric Functions Long Questions (Question 1 - 3)

Question 1:
(a) Sketch the graph of y = cos 2x for 0°  x  180°.
(b) Hence, by drawing a suitable straight line on the same axes, find the number of
solutions satisfying the equation for 0°  x  180°.

Solution:
(a)(b)

Question 2:
(a) Sketch the graph of
(b) Hence, using the same axes, sketch a suitable straight line to find the number of
solutions to the equation
State the number of solutions.

Solution:
(a)(b)

Question 3:
(a) Prove that $\frac{2\mathrm{tan}x}{2-{\mathrm{sec}}^{2}x}=\mathrm{tan}2x.$ .
(b)(i) Sketch the graph of y = – tan 2x for 0  x ≤ p .
(b)(ii) Hence, by drawing a suitable straight line on the same axes, find the number of solutions satisfying the equation $\frac{3x}{\pi }+\frac{2\mathrm{tan}x}{2-{\mathrm{sec}}^{2}x}=0$  for 0  x  p .
State the number of solutions.

Solution:
(a)

(b)(i)

(b)(ii)

When x = 0, y = 0.
When x = p, y = 3.
Number of solutions = 3