Evaluating for the sine of an angle using the difference formula

The video tutorial explains how to find the sine of 105 degrees using angle subtraction. It begins by rewriting 105 degrees as 135 degrees minus 30 degrees and introduces the sine subtraction formula. The instructor clarifies the formula's application, emphasizing the importance of understanding angle subtraction. The unit circle is used to evaluate the angles, and the final calculations are demonstrated, resulting in the sine of 105 degrees. The lesson concludes with factoring and simplifying the result.

What is the purpose of rewriting 105 degrees as 135 degrees minus 30 degrees?

• To use the sine difference formula

• To convert degrees to radians

• To find an equivalent angle in the first quadrant

• To simplify the calculation of cosine

In the sine difference formula, what is the role of angle V?

• It is added to angle U

• It is always a negative angle

• It is subtracted from angle U

• It is the same as angle U

How is the angle 135 degrees represented on the unit circle?

• As -sqrt 2 / 2, sqrt 2 / 2

• As 1/2, sqrt 3 / 2

• As sqrt 3 / 2, 1/2

• As sqrt 2 / 2, -sqrt 2 / 2

What is the sine of 30 degrees according to the unit circle?

• -1/2

• sqrt 2 / 2

• sqrt 3 / 2

• 1/2

What common factor is extracted in the final simplification of the expression?

• sqrt 2

• sqrt 3

• 1/2

• 4