Problem 1 Using the Unit Circle

Multiple Choice What is cos − 1 ( 1 2 ) cosine minus 1 . open , 1 half , close in degrees?

1. − 60 ° negative 60 degrees
2. 30°
3. 60°
4. 300°

Draw a unit circle and mark each point on the circle that has x-coordinate 1 2 . 1 half , . These points and the origin form 30 ° − 60 ° − 90 ° 30 degrees , minus 60 degrees negative 90 degrees triangles.

The simplest domain values for cosine that allow cosine to have values from − 1 negative 1 to 1 are the angles in the top half of the unit circle.

Thus, even though

cos 60 ° = cos 300 ° = cos ( − 60 ° ) , cosine , 60 degrees equals cosine , 300 degrees equals cosine open negative 60 degrees close comma

cos − 1 ( 1 2 ) cosine super negative 1 end super . open , 1 half , close must be 60 ° . 60 degrees . The correct choice is C.

Image Long Description