Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant. tan⁡t,cos⁡t; Quadrant III

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izboknil3 · Accepted Answer

We are given tan⁡t and need to rewrite the expression in terms of cos⁡t. Using the reciprocal identity, we get tan⁡t=sin⁡tcos⁡t so we need to rewrite the sine in terms of cosine. Using the Pythagorean Identity, we get: sin2t+cos2t=1 Pythagorean Identity. sin2t=1−cos2t Subtract cos2t on both sides. sin⁡t=±1−cos2t Square root both sides. Since t lies in Quadrant lll, then sin⁡t&amp;lt;0 so we need to use the negative root. Therefore, tan⁡t=sin⁡tcos⁡t=−1−cos2tcos⁡t Result: tan⁡t=−1−cos2tcos⁡t

Write the first expression in terms of the second if the terminal point determin

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