Question

F the ratio of sine of an angle to its cosine is 3 : 4, then find their actual values.

Answer 1

Answer:

See below.

Step-by-step explanation:

Let the angle be theta, then,

$\frac{sin \theta}{cos \theta} = \frac{3}{4}$

Squaring on both the sides,

$\frac{sin^2 \theta}{cos^2 \theta} = \frac{9}{16}$

By Componendo,

$\frac{sin^2 \theta + cos^2 \theta}{ cos^2 \theta} = \frac{25}{16}$

We know that,

$sin^2 \theta + cos^2 \theta = 1$

We substitute this value,

$\frac{1}{cos^2 \theta} = \frac{25}{16}$

We get,

$cos \theta = \frac{4}{5}$

Therefore,

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