Question

Find the value of tan Θ is sin Θ = 1/2 90° ≤ Θ ≤ 180°

a. -√3/2
b. -√3/3
c. √3/2
d. √3/3

Answer 1

sin theta=p/h=1/2 let p=1k and h=2k

tan theta=p/b=1k/(√(2k)²-k²)=1k/k√3=1/√3

=tan 30

therefore theta =30°

your answer is 1/√3=√3/3

Answer 2

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Answer:

b. -√3/3

Explanation:

From your knowledge of the values of trig functions of special angles, you know sin(30°) = 1/2. For an angle in the second quadrant, this means the reference angle is 30° and the actual angle measure is 180° -30° = 150°.

The corresponding value of the tangent function is -√3/3, negative in the second quadrant.