Question

5*sin theta=3, find cos theta

Answer 1

Answer:

The value of cos θ is $\frac{4}{5}$.

Step-by-step explanation:

It is provided that $5sin\theta=3$.

The value of sin θ is:

$5sin\theta=3\\sin\theta=\frac{3}{5}$

Use the trigonometric identity: $sin^{2}\theta + cos^{2}\theta=1$ to determine the value of cos θ.

$sin^{2}\theta + cos^{2}\theta=1\\(\frac{3}{5} )^{2} + cos^{2}\theta=1\\cos^{2}\theta=1-\frac{9}{25}\\ cos^{2}\theta=\frac{16}{25} \\cos\theta=\sqrt{\frac{16}{25}}\\=\frac{4}{5}$

Thus, the value of cos θ is $\frac{4}{5}$.