To find the exact values of cos 150° and sin 150°, we can use the properties of trigonometric functions and the unit circle.
First, note that 150° is in the second quadrant. In the second quadrant, the cosine function is negative, and the sine function is positive.
We can express 150° as follows:
- 150° = 180° – 30°
Using the cosine and sine subtraction identities:
- cos(180° – θ) = -cos(θ)
- sin(180° – θ) = sin(θ)
Now, we can substitute θ = 30°:
- cos(150°) = cos(180° – 30°) = -cos(30°) = -√3/2
- sin(150°) = sin(180° – 30°) = sin(30°) = 1/2
Thus, the exact values are:
- cos 150° = -√3/2
- sin 150° = 1/2