Question

What are the sine, cosine, and tangent of 5 pi over 4 radians?

Answer 1

Let us first convert the radians into degrees.

5π/4 radians = 5* 180 / 4 degrees
= (5 * 45)°
= 225°

sin 225⁰ = sin (180+45)°
The angle will lie in the third quadrant, where sine value is negative.
Thus, sin 225° = - sin 45⁰
= $\frac{-1}{ \sqrt{2} }$

cos 225⁰ = cos (180+45)°
The angle will lie in the third quadrant, where cosine value is negative.
Thus, cos 225° = - cos 45⁰
= $\frac{-1}{ \sqrt{2} }$

tan 225⁰ = tan (180+45)°
The angle will lie in the third quadrant, where tangent value is positive.
Thus, tan 225° =  tan 45⁰
= 1