Question

If sin theta = -½ and theta lies in Quadrant IV , find the value of all the other five trigonometric functions. ​

Answer 1

SOLUTION :-

Given that,

θ € 4th quadrant

3π/2 < θ < 2π

And

sin θ = - 1/2

We know,

sin²θ + cos²θ = 1

[ -1/2] ² + cos²θ = 1

1/4 + cos²θ = 1

cos²θ = 1 - 1/4

cos²θ = 4 - 1 / 4

cos²θ = 3/4

cos²θ = + √3/2

As,

θ € 4th quadrant = cos θ > 0

cosθ = √3/2

tan θ = sin θ / cos θ

tan θ = 1/2 ÷ √3/2

tan θ = - 1/√3

Now,

cosec θ = 1/sin θ = -2

sec θ = 1/cos θ = 2√3

cot θ = 1/tan θ = - √3