# Lecture - 11 Chapter 3 Trigonometric Functions

Derivation for half angles, sin(x/2), cos(x/2) and tan(x/2)

Example 27 Find the value of \tan \frac{\pi}{8}

Example 28 If \tan x = \frac {3}{4}, \pi < x < \frac{3\pi}{2}, find the value of sin(x/2), cos(x/2) and tan(x/2).

Find sin(x/2), cos(x/2) and tan(x/2) in each of the following:

Question 8 \tan x = \frac{-4}{3}, *x * in the quadrant II.

Question 9 \cos x = \frac{-1}{3}, *x * in the quadrant III.

Question 10 \sin x = \frac{1}{4}, *x * in the quadrant II.

Example 29 Prove that \cos^2 x + \cos^2 \left ( x + \frac{\pi}{3} \right ) + \cos^2 \left ( x – \frac{\pi}{3} \right ) = \frac{3}{2}