Find the exact values of cos 150° and sin 150°?

To find the exact values of cos 150° and sin 150°, we will use the trigonometric identity cos (180° - Θ) and sin (180° - Θ).

Answer: The exact value of cos (150^∘) is −√3/2 and sin (150^∘) is 1/2.

Now, let us understand the way in which we can find the value of cos 150° and sin 150°.

Explanation:

For cos 150°,

By using cos (180° – Θ) =  –  cos Θ

⇒ cos (180° -30°)  

⇒ – cos 30^∘ 

As we know that cos 30° = √3 / 2 

Therefore, cos 150° =  –  cos 30°  =  - √3 / 2

For sin 150°,

By using sin (180° – Θ) = sin Θ, we get

⇒ sin (180^∘ − 30^∘ )   

⇒ sin 30^∘

As we know that sin 30^∘ = 1 / 2

Therefore, the value of sin 150^∘ = 1 / 2

Thus, the exact value of cos (150^∘) is − √3/2 and sin (150^∘) is 1/2.