A function value and a quadrant are given. Find the other five function values. Give exact answers, uing radicals as needed. Rationalize all denominators. cot⁡θ=−4, Quandrant 4

Question

A function value and a quadrant are given. Find the other five function values. Give exact answers, uing radicals as needed. Rationalize all denominators.  cot⁡θ=−4, Quandrant 4

Arnold Odonnell · Accepted Answer

It is given that, cot⁡θ=−4  Compute the other five functional values as follows.  csc2θ−cot2θ=1  csc⁡θ=1+cot2θ  csc⁡θ=1+(−4)2  csc⁡θ=−17  Compute the value of sin⁡θ as follows.  sin⁡θ=1csc⁡θ  sin⁡θ=−117  sin⁡θ=−1717  Compute the value of cos⁡θ as follows.  cot⁡θ=cos⁡θsin⁡θ  cos⁡θ=cot⁡θ⋅sin⁡θ  cos⁡θ=−4(−1717)  cos⁡θ=41717  Compute the value of sec⁡θ as follows.  sec⁡θ=1cos⁡θ  sec⁡θ=17417  sec⁡θ=174  Compute the value of tan⁡θ as follows.  tan⁡θ=1cot⁡θ  tan⁡θ=−14

A function value and a quadrant are given. Find the other five function values.

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