What is the exact value of sine of open paren 345 degrees close paren ?
Answer
A
the fraction with numerator square root of 3 plus square root of 2 and denominator 2
B
the fraction with numerator negative square root of 3 plus square root of 2 and denominator 2
C
the fraction with numerator negative square root of 6 plus square root of 2 and denominator 4
D
the fraction with numerator square root of 6 plus square root of 2 and denominator 4
Explanation
Since 345° = 360° − 15°, its sine is −sin 15°. Using the angle-difference identity, sin 15° = (√6 − √2)/4, so sin 345° = (−√6 + √2)/4. This matches choice A.
AI-written and checked against the verified answer.