If cot⁡(θ)=7, what is sin⁡(θ),cos⁡(θ),sec⁡(θ) between 0 and 2π?

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averes8 · Accepted Answer

Draw a right-angled triangle ABC where B is 90 deg, A is $θ . \cot (θ) = A \frac{B}{B} C = 7 . A C = \sqrt{7^{2} + 1} = 5 \sqrt{2} . A B = 7, B C = 1 .$
$\sin (θ) = B \frac{C}{A} C = \frac{1}{5} \sqrt{2} = 0.2 \frac{\sqrt{2}}{2} = 0.1 \sqrt{2} = 0.1414 .$
$\cos (θ) = \frac{7}{5} \sqrt{2} = 1.4 \frac{\sqrt{2}}{2} = 0.7 \sqrt{2} = 0.9899 .$
$\sec (θ) = \frac{1}{\cos (θ)} = 5 \frac{\sqrt{2}}{7} = 1.0102$ . These are all approximate values and apply to quadrant 1. $\cot (θ) = \frac{7}{1}$ in quadrant 1, or $- \frac{7}{- 1}$ in quadrant 3. In this quadrant sin, cos, sec are all negative, so $\sin (θ) = - 0.1414, \cos (θ) = - 0.9899, \sec (θ) = - 1.0102$ in QIII, and 0.1414, 0.9899, 1.0102 in QI.

If cot(theta)=7, what is sin(theta), cos(theta), sec(theta) between 0 and 2 pi?

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