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

Question

Mathematics

Carley Murillo

16 March, 06:05

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

+2

Answers (1)

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Fernanda Bailey · Answer 1

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

Step-by-step 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