Write every given trigonometric function: 1. tan⁡θ,cos⁡θ in Quadrant III 2. cot⁡θ,sin⁡θ in Quadrant II 3. cos⁡θ,sin⁡θ in Quadrant IV 4. sec⁡θ,sin⁡θ in Quadrant I 5. sec⁡θ,tan⁡θ in Quadrant II 6. csc⁡θ,cot⁡θ in Quadrant

Question

Write every given trigonometric function:  1. tan⁡θ,cos⁡θ in Quadrant III  2. cot⁡θ,sin⁡θ in Quadrant II  3. cos⁡θ,sin⁡θ in Quadrant IV  4. sec⁡θ,sin⁡θ in Quadrant I  5. sec⁡θ,tan⁡θ in Quadrant II  6. csc⁡θ,cot⁡θ in Quadrant

Alannej · Accepted Answer

1. sin2θ+cos2θ=1  cos⁡θ=±1−sin2θ  2. cos⁡θ=−1−sin2θ  We know:  tan⁡θ=sin⁡θcos⁡θ  So, tan⁡θ=−sin⁡θ1−sin2θ  3. sin2θ+cos2θ=1  cos⁡θ=±1−sin2θ  4. cos⁡θ=−1−sin2θ  We know:  θ=cos⁡θsin⁡θ  5. sin2θ+cos2θ=1  sin⁡θ=±1−cos2θ  6. sin⁡θ=−1−cos2θ

Write every given trigonometric function: 1. tantheta, costheta in Quadrant III 2. cottheta, sintheta in Quadrant II

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