Question

If sine theta equals one half and pi over two is less than theta is less than pi, what are the values of cos Θ and tan Θ?

cosine theta equals negative square root of three over two; tangent theta equals negative square root of three over three

cosine theta equals square root of three over two; tangent theta equals square root of three over three

cosine theta equals negative square root of three over two; tangent theta equals square root of three over three

cosine theta equals square root of three over two; tangent theta equals negative square root of three over three

Answer 1

cos(5π/6) = -(√3)/2

tan(5π/6) = -(√3)/3

Explanation:

Answer 2

cosine theta equals negative square root of three over two; tangent theta equals negative square root of three over three

Explanation:

If the angle were a 1st-quadrant angle, it would be ...

arcsin(1/2) = π/6

and the other functions would be ...

cos(π/6) = (√3)/2

tan(π/6) = 1/√3 = (√3)/3

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The angle of interest is in the second quadrant, where the signs of cosine and tangent are negative. Hence, ...

• θ = 5π/6
• cos(5π/6) = -(√3)/2
• tan(5π/6) = -(√3)/3