Question

What is the sine value of 7pi/6

A. - sqrt 3 over 2
B. Sqrt 3 over 2
C. - 1/2
D. 1/2

Answer 1

C -
`(1)/(2)`

sin(7π / 6 )

note 7π\6 is in the third quadrant where sin is negative

the related acute angle to 7π/6 is 7π/6 - π = π/6

sin (7π/6) = - sin(π/6) = -
`(1)/(2)`

Answer 2

C. -1/2

Explanation:

7π/6 radians is equivalent to (7π/6)(180°/π) = 210°, a 3rd-quadrant angle whose reference angle is 30°. The sine of angles in the 3rd quadrant is negative.

sin(30°) = 1/2

sin(210°) = -sin(30°) = -1/2

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In radians mode, your calculator can tell you this result directly.