Question

Find an exact value.

sine of negative eleven pi divided by twelve.
quantity square root of six plus square root of two divided by four.
quantity negative square root of six minus square root of two divided by four.
quantity square root of two minus square root of six divided by four.
quantity square root of six minus square root of two divided by four.

Answer 1

(√2 − √6) / 4

Explanation:

Rewrite using special angles.

sin(-11π/12)

sin((4−15)π/12)

sin(4π/12 − 15π/12)

sin(π/3 − 5π/4)

Use angle difference formula:

sin(π/3) cos(5π/4) − sin(5π/4) cos(π/3)

Evaluate:

(√3/2) (-√2/2) − (-√2/2) (1/2)

-√6/4 + √2/4

(√2 − √6) / 4