How do you express in terms of angles less than 90 degrees?

sin 120 degrees
cos 150 degrees
tan 280 degrees

Always ask yourself,

1. What quadrant is the angle in? That determines the ± according to the CAST rul
2. "How far is it to the x-axis"?

sin 120° = sin60
cos150° = -cos 30
tan 280° = -tan 80°

Sin (180 - A) = sin A. (angle in degrees)

sin 120 = sin (180 - 60) = sin 60

Cos (180 - A) = - cos A
cos 150 = cos (180 - 30) = - cos 30

tan (360 - A) = - tan A,
tan 280 = tan (360 - 80) = - tan 80

To express trigonometric functions in terms of angles less than 90 degrees, you can use the following properties:

1. Sine: The sine function is positive in the second and third quadrants of the unit circle. Since 120 degrees is located in the second quadrant, you can express sin 120 degrees as the negative value of the sine of the reference angle in the first quadrant, which is 60 degrees.

Therefore, sin 120 degrees = - sin 60 degrees.

2. Cosine: The cosine function is negative in the second and third quadrants of the unit circle. Since 150 degrees is located in the second quadrant, you can express cos 150 degrees as the negative value of the cosine of the reference angle in the first quadrant, which is 30 degrees.

Therefore, cos 150 degrees = - cos 30 degrees.

3. Tangent: The tangent function is positive in the first and third quadrants of the unit circle. Since 280 degrees is located in the third quadrant, you can express tan 280 degrees as the negative value of the tangent of the reference angle in the first quadrant, which is 100 degrees.

Therefore, tan 280 degrees = - tan 100 degrees.

You can then evaluate the trigonometric functions of the reference angles using a calculator or reference table.