Question

If sin theta=3/4 then, cos theta and cot theta. Find value​

Answer 1

Step-by-step explanation:

$\sin\theta = \frac{3}{4} = \frac{perpendicular}{hypotenuse} \\ in \: a \: right \: triangle \: \\ hypotenuse = 4 \: unit \\ perpendicular = 3 \: unit \\ base = to \: find\\ base \: = \sqrt{ {hypotenuse}^{2} - {perpendicular}^{2} } \\ = \sqrt{ {4}^{2} - {3}^{2} } \\ = \sqrt{16 - 9} \\ = \sqrt{7} \: unit \\ \\ so \: \cos \theta = \frac{base}{hypotenuse} \\ = \frac{ \sqrt{7} }{4} \\ \cot \theta = \frac{ \cos \theta }{\ \sin\theta} = \frac{ \frac{ \sqrt{7} }{4} }{ \frac{3}{4} } \\ \cot \theta = \frac{ \sqrt{7} }{4} \times \frac{4}{3} = \frac{ \sqrt{7} }{3}$

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Answer 2

sin^2theta + cos^2theta =1
(3/4)^2-1=-cos^2theta
(9/16)-1 = -cos^2theta
-7/16= -cos^2theta
cos^2theta=7/16
cos theta=root7/4