Answer :
The value of [tex]\csc \theta[/tex] is [tex]\frac{5}{4}[/tex]
Explanation:
Given that the function [tex]cos \ \theta[/tex] is [tex]cos \ \theta= \frac{3}{5}[/tex]
We need to determine the value of [tex]\csc \theta[/tex]
The value of Opposite side of the triangle:
The formula for [tex]cos \ \theta[/tex] is given by
[tex]cos \ \theta= \frac{adj}{hyp}=\frac{3}{5}[/tex]
The value of opposite side can be determined using the formula,
[tex]opp=\sqrt{hyp^2-adj^2[/tex]
[tex]opp=\sqrt{5^2-3^2}[/tex]
[tex]opp=\sqrt{25-9}[/tex]
[tex]opp=\sqrt{16}=4[/tex]
Thus, the value of opposite side is 4
The value of [tex]sin \ \theta[/tex]:
The formula for [tex]sin \ \theta[/tex] is given by
[tex]sin \ \theta= \frac{opp}{hyp}[/tex]
Substituting the values, we have,
[tex]sin \ \theta= \frac{4}{5}[/tex]
Thus, the value of [tex]sin \ \theta[/tex] is [tex]\frac{4}{5}[/tex]
The value of [tex]\csc \theta[/tex]:
The formula for [tex]\csc \theta[/tex] is given by
[tex]csc \ \theta=\frac{1}{sin \ \theta}[/tex]
Substituting the values, we have,
[tex]csc \ \theta=\frac{1}{\frac{4}{5}}[/tex]
[tex]csc\ \theta= \frac{5}{4}[/tex]
Thus, the value of [tex]\csc \theta[/tex] is [tex]\frac{5}{4}[/tex]
Hence, the value of [tex]\csc \theta[/tex] is [tex]\frac{5}{4}[/tex]