Circular Trigonometry Question

Question

Find an exact value by using an appropriate addition or subtraction formula.

Find the exact value for cos 15°

Which answer is it

A:√6 - √2 /4

B: √6 + √2 /4

C: -√2 - √6 /4

D: √2 - √6 /4

Answer 1

cos(15°) could be calculated in many ways using formulas for cosine of difference of angles, either cos(60°-45°) or cos(45°-30°). Results should be the same. Let's take the first one:

cos(60°-45°) = cos(60°)cos(45°)+sin(60°)sin(45°) = 1/2*√2/2+√3/2*√2/2=√2/4+√6/4=(√2+√6)/4

Mathematically speaking none of the proposed answers is correct, but since one option should be selected the closest would be option B, which is missing parentheses.

Answer 2

Think of angles that you know sin and cos for and the formulas that combine them. Two obvious ones should occur to you - cos(30°/2) and cos(45° - 30°); we shall use the latter.

cos(45° - 30°) = cos(45°)cos(30°) + sin(45°)sin(30°) = √2/2 * √3/2+ √2/2 * 1/2 =

√6/4 + √2/4 =

(√6 + √2)/4

B