Find exact value of each trigometric function.

tan 60
sin225
cos 135
tan 150
tan240
sin 90
cos 150
cos90

To find the exact values of trigonometric functions, we can make use of the unit circle and the special angles associated with it.

1. tan 60:
- Start by locating the angle 60 degrees on the unit circle.
- Since tan is equal to sin/cos, we need to find the sin and cos values of 60 degrees.
- For 60 degrees, the sin value is √3/2 and the cos value is 1/2.
- Therefore, tan 60 = sin 60 / cos 60 = (√3/2) / (1/2) = √3.

2. sin 225:
- Locate the angle 225 degrees on the unit circle.
- Notice that 225 degrees is in the third quadrant, where sine values are negative.
- The sin value of 225 degrees is -√2/2.

3. cos 135:
- Locate the angle 135 degrees on the unit circle.
- Notice that 135 degrees is in the second quadrant, where cosine values are negative.
- The cos value of 135 degrees is -√2/2.

4. tan 150:
- Locate the angle 150 degrees on the unit circle.
- The sin value of 150 degrees is 1/2, and the cos value is -√3/2.
- Therefore, tan 150 = sin 150 / cos 150 = (1/2) / (-√3/2) = -1/√3 = -√3/3.

5. tan 240:
- Locate the angle 240 degrees on the unit circle.
- The sin value of 240 degrees is -√3/2, and the cos value is -1/2.
- Therefore, tan 240 = sin 240 / cos 240 = (-√3/2) / (-1/2) = √3.

6. sin 90:
- Locate the angle 90 degrees on the unit circle.
- The sin value of 90 degrees is 1.

7. cos 150:
- Locate the angle 150 degrees on the unit circle.
- The cos value of 150 degrees is -√3/2.

8. cos 90:
- Locate the angle 90 degrees on the unit circle.
- The cos value of 90 degrees is 0.