Question

If sinƟ = - 4/5 and Ɵ lies in the third quadrant, then the

value of cos Ɵ/2 is

A) 1/5

B) 1/√5

C) 1/2

D) -1/2 ​

Answer 1

Step-by-step explanation:

• Given If sin Ɵ = - 4/5 and Ɵ lies in the third quadrant, then the value of cos Ɵ / 2 is
• Now sin theta = - 4/5
• Now we know it is in the third quadrant and sin and cos are negative.
• So if we consider a triangle in which AC^2 = AB^2 + BC^2
• We get 5^2 = 4^2 + x^2
• Or 25 – 16 = x^2
• Or x^2 = 9
• Or x = 3
• So in the third quadrant cos theta is negative.So cos theta = - 3/5
• Now theta lies between π and 3π / 2
• Also theta / 2 lies between π / 2 and 3π / 4
• So cos theta / 2 will be negative.
• Now sin theta = - 4/5
• So cos theta = 2 cos^2 theta / 2 – 1
• So – 3/5 = 2 cos^2 theta / 2 – 1
• So 2 cos^2 theta / 2 = 1 – 3/5
•                                   = 2/5
• So cos theta / 2 = 1/√5 and – 1/√5
• So cos theta / 2 will be negative and so it will be – 1/√5

Therefore cos theta / 2 = - 1/√5

Reference link will be

https://brainly.in/question/3140256