Question

Use the unit circle to find the following values.

1. sin 150
2. tan 315
3. cot 11pi/6
4. cos 2pi/3

Answer 1

The unit circle can be used to find sin 150°, tan 315°, cot 11pi/6, and cos 2pi/3 by considering their reference angles and the signs of trigonometric functions in various quadrants.

Step-by-step explanation:

We will use the unit circle to find the values of sine, tangent, cotangent, and cosine for specific angles.

1. sin 150°: On the unit circle, 150° is in the second quadrant where sine values are positive. We have sin 150° = sin(180° - 30°) = sin 30° = 1/2.
2. tan 315°: This angle is in the fourth quadrant where the tangent values are positive. By using the reference angle of 45°, we find tan 315° = tan(360° - 45°) = tan 45° = 1.
3. cot 11pi/6°: To find cotangent, which is the reciprocal of the tangent, we use the reference angle of pi/6. We know that tan(pi/6) = 1/√3 and thus cot(11pi/6) = √3.
4. cos 2pi/3°: In the second quadrant, the cosine values are negative, and the reference angle is pi/3. Therefore, cos 2pi/3 = cos(pi - pi/3) = -cos(pi/3) = -1/2.

Answer 2

Where is the circle