Question

Let sin(30°) ½ Write an angle measure (B) in degrees, where cos (B)=½

Answer 1

To find angle B where cos(B) = ½, we use standard trigonometric identities and know that B can be 60° or 300°, as cosine has these values at those angles.

Step-by-step explanation:

The student is asked to find an angle measure, B, such that cos(B) = ½. We know from trigonometric principles that cosine function has a value of ½ at specific standard angles. The angles where cos(B) = ½ are at 60° and 300° (or equivalently, -60° if we consider negative angles), because cosine is positive in the first and fourth quadrants of the unit circle.

Here's a step-by-step solution:

1. Recognize that cos(60°) = ½. This is a well-known trigonometric identity.
2. Also, acknowledge that cosine is periodic and symmetric about the y-axis, meaning cos(360° - 60°) = cos(300°) = ½.
3. Select either 60° or 300° as the possible values for angle B that satisfy the equation cos(B) = ½.