Question

Trigonometry Trigonometric Functions Given: Cos θ = (3/5), Find: Csc θ

Answer 1

The value of $\csc \theta$ is $\frac{5}{4}$

Explanation:

Given that the function $cos \ \theta$ is $cos \ \theta= \frac{3}{5}$

We need to determine the value of $\csc \theta$

The value of Opposite side of the triangle:

The formula for $cos \ \theta$ is given by

$cos \ \theta= \frac{adj}{hyp}=\frac{3}{5}$

The value of opposite side can be determined using the formula,

$opp=\sqrt{hyp^2-adj^2$

$opp=\sqrt{5^2-3^2}$

$opp=\sqrt{25-9}$

$opp=\sqrt{16}=4$

Thus, the value of opposite side is 4

The value of $\csc \theta$:

The formula for $\csc \theta$ is given by

$csc \ \theta=\frac{1}{sin \ \theta}$

First, we shall determine the value of $sin \ \theta$

The formula for $sin \ \theta$ is given by

$sin \ \theta= \frac{opp}{hyp}$

Substituting the values, we have,

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

Thus, the value of $sin \ \theta$ is $\frac{4}{5}$

Substituting the values in the formula for $\csc \theta$ , we have,

$csc \ \theta=\frac{1}{\frac{4}{5}}$

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

Hence, the value of $\csc \theta$ is $\frac{5}{4}$