7
QuizMultiple Choice

Trigonometric Difference Identities — Quiz

Question 7 • Precalculus

What is the exact value of sine of open paren 7 pi over 12 close paren ?

Answer
A
the fraction with numerator square root of 6 plus square root of 2 and denominator 4
B
the fraction with numerator square root of 6 minus square root of 2 and denominator 4
C
the fraction with numerator square root of 6 minus square root of 2 and denominator 8
D
the fraction with numerator square root of 6 plus square root of 2 and denominator 8

Explanation

Rewrite 7π/12 as π/3 + π/4, or 60° + 45°. Using the sine addition formula, sin(60° + 45°) = sin 60° cos 45° + cos 60° sin 45° = (√6 + √2)/4. Therefore, the exact value is choice A.

AI-written and checked against the verified answer.

Previous
Next