Question

if tan theta equals to minus 4 by 3 then sin theta equals to ​

Answer 1

Given

tan x = -4/3

→1/tan x = -3/4

→cot x = - 3/4

Using the identity, cosec²∅ - cot²∅ = 1

$\sf{cosec {}^{2}x - cot {}^{2}x = 1} \\ \\ \implies \sf{cosec \: x \: = \sqrt{1 + cot {}^{2}x } } \\ \\ \implies \: \sf{cosec \: x = \sqrt{1 + ( \frac{ - 3}{4}) {}^{2} } } \\ \\ \implies \: \boxed{\sf{cosec \: x \: = \frac{5}{4} }}$

Since, sin x = 1/cosec x

$\sf{sin \: x \: = \: \frac{1}{ \frac{5}{4} }} \\ \\ \implies \: \boxed{ \sf{sin \: x \: = \frac{4}{5} }}$

Answer 2

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