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

sin 120 degrees
cos 150 degrees
tan 280 degrees

180-120=60

To express trigonometric functions such as sine, cosine, and tangent in terms of angles less than 90 degrees, we need to use the concept of reference angles. A reference angle is the acute angle formed between the terminal side of the angle and the x-axis.

Let's calculate the reference angles for the given angles:

1. sin 120 degrees:
To find the reference angle, we subtract the angle from 180 degrees because 120 degrees is in the second quadrant. Therefore, the reference angle is 180 - 120 = 60 degrees.
Since the sine function is positive in the second and third quadrants, sin 120 degrees is equal to sin 60 degrees.

2. cos 150 degrees:
The reference angle is obtained by subtracting the angle from 180 degrees since 150 degrees is in the second quadrant. So, the reference angle is 180 - 150 = 30 degrees.
Since the cosine function is only positive in the fourth quadrant, cos 150 degrees is equal to -cos 30 degrees.

3. tan 280 degrees:
We determine the reference angle by subtracting 180 degrees from the given angle since 280 degrees is in the third quadrant. Hence, the reference angle is 280 - 180 = 100 degrees.
Since the tangent function is negative in the second and fourth quadrants, tan 280 degrees is equal to -tan 100 degrees.

So, to express the trigonometric functions in terms of angles less than 90 degrees:
- sin 120 degrees = sin 60 degrees
- cos 150 degrees = -cos 30 degrees
- tan 280 degrees = -tan 100 degrees