Pre-Calculus - How to use the addition formula for two angles of sine cos105

The video tutorial explains how to find the sine of 105 degrees by decomposing it into known angles using the sum and difference formulas. The instructor demonstrates how to use the unit circle to determine the sine and cosine values of 60 and 45 degrees, and then simplifies the expression to find the final result.

Why is it necessary to express 105 degrees as a sum of known angles?

• To simplify the calculation using a calculator

• To find the exact value on the unit circle

• To convert it into radians

• To use the sum and difference formulas

Which angles are used to express 105 degrees in the sum and difference formula?

• 90 and 15 degrees

• 45 and 60 degrees

• 60 and 45 degrees

• 30 and 75 degrees

What is the sine of 60 degrees according to the unit circle?

• 1/2

• √3/2

• 0

• √2/2

What is the cosine of 45 degrees according to the unit circle?

• 0

• 1/2

• √3/2

• √2/2

What common factor is extracted during the simplification of the sine of 105 degrees?

• √6/4

• √2/4

• 1/2

• √3/2