Find the exact value of each of the remaining trigonometric function of θ. cos⁡θ=2425,270∘&lt;θ&lt;360∘ sin⁡θ=? tan⁡θ=? sec⁡θ=? csc⁡θ=? cot⁡θ=?

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Find the exact value of each of the remaining trigonometric function of θ. cos⁡θ=2425,270∘&amp;lt;θ&amp;lt;360∘ sin⁡θ=? tan⁡θ=? sec⁡θ=? csc⁡θ=? cot⁡θ=?

Ayesha Gomez · Accepted Answer

Step 1 Given: cos⁡θ=2425,270∘&amp;lt;θ&amp;lt;360∘ So the angle lies in fourth quadrant. In the fourth quadrant cosine and secant are positive all others are negative. Pythagorean identity is used for finding sine value sin2θ+cos2θ=1 sin⁡θ=±1−cos2θ =±1−(2425)2 =±252−242252 =−725 The sine value is negative since angle is in third quadrant. Step 2 The tan value can be found as tan⁡θ=sin⁡θcos⁡θ =−7252425 =−724 Step 3 Secant is reciprocal of cosine. sec⁡θ=1cos⁡θ =12425 =2524 Step 4 Cosecant is the reciprocal of sine. csc⁡θ=1sin⁡θ =1−725 =−257 Step 5 Cot is the reciprocal of tan cot⁡θ=1tan⁡θ =1−724 =−247

Find the exact value of each of the remaining trigonometric function of theta.displaystyle

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