Question

if 4 cos theta = 3 then find sin theta and tan theta​

Answer 1

GIVEN :–

$\\ \implies \rm 4 \cos(\theta) = 3$

TO FIND :–

• Value of tan(θ) & sin(θ) = ?

SOLUTION :–

$\\ \implies \rm 4 \cos(\theta) = 3$

$\\ \implies \rm \cos(\theta) = \dfrac{3}{4}$

• We know that –

$\\ \longrightarrow \sf \green {\sin^{2}( \theta) + \cos^{2} (\theta) = 1}$

$\\ \implies \tt {\sin^{2}( \theta) + \left ( \dfrac{3}{4} \right)^{2} = 1}$

$\\ \implies \tt {\sin^{2}( \theta) +\dfrac{9}{16}= 1}$

$\\ \implies \tt \sin^{2}( \theta) = 1 - \dfrac{9}{16}$

$\\ \implies \tt \sin^{2}( \theta) = \dfrac{16 - 9}{16}$

$\\ \implies \tt \sin^{2}( \theta) = \dfrac{7}{16}$

$\\ \implies \tt \sin( \theta) = \pm \sqrt \dfrac{7}{16}$

$\\ \implies \large \red{ \boxed{\tt \sin( \theta) = \pm \dfrac{ \sqrt7}{4}}}$

• We also know that —

$\\ \longrightarrow \sf \green { \tan( \theta) = \dfrac{ \sin( \theta) }{ \cos( \theta) } }$

$\\ \implies \tt { \tan( \theta) = \dfrac{\pm \dfrac{ \sqrt7}{4}}{\dfrac{3}{4}}}$

$\\ \implies \large\red { \boxed{\tt { \tan( \theta) = \pm\dfrac{\sqrt{7} }{3}}}}$

Answer 2

$\huge\mathfrak\red{hello}$

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WE HAVE TO FIND Sin theta and tan theta

‣Answer彡

➣see attachment

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hope it helps you✌

THANKS❤