Question

Suppose cotangent (theta) = startfraction 5 over 12 endfraction, where pi less-than theta less-than startfraction 3 pi over 2 endfraction. what is sin(θ)?

Answer 1

sin(Q) = -(12/13)

What are trigonometric ratios?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.  It is a branch of mathematics that deals with the relation between the angles and sides of a right-angled triangle.

cot(Q) = 5/12

sin(Q) = 1/cosec(Q)

$sin(Q) = \frac{1}{\sqrt{1+{cot}^2(Q)}}\\sin(Q) = \frac{1}{\sqrt{1+\frac{25}{144}}}\\sin(Q) = \frac{1}{\sqrt{\frac{169}{144}}}$

sin(Q) = ±12/13

Because, π < Q < (3/2)π

Therefore, sin(Q) = -12/13

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