Question

If tan θ = 4/3, then sinθ is: *


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Answer 1

Answer:

the correct answer is 4/5

Step-by-step explanation:

Answer 2

$\mathfrak{\underline{Answer :-}}$

Given:

• $tan\theta = \dfrac{4}{3}$
• $sin\theta = ?$

Solution:

$tan \ theta = \dfrac{4}{3}$

$\implies \dfrac{sin \theta}{cos \theta} = \dfrac{4}{3}$

$\implies cos \theta = \dfrac{3}{4} sin \theta$

$\boxed{sin^2 \theta + cos^2 \theta = 1}$

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

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

$\implies \dfrac{25}{16} sin^2\theta = 1$

$\implies sin^2 \theta = \dfrac{16}{25}$

$\boxed{\implies{\boxed{sin \theta = \dfrac{4}{5}}}}$