Given:
The point is (0.6, 0.8).
The circle is unit circle.
[tex]The\text{ angle is }\theta.[/tex]
Aim:
[tex]We\text{ need to find }cos\theta,sin\theta\text{ and }cot\theta.[/tex]
Explanation:
The formula to find the sin theta is
[tex]sin\theta=\frac{y}{r}[/tex][tex]where\text{ }r=\sqrt{x^2+y^2}.[/tex]
Substitute x =0.6 and y =0.8 in the equaion to find r.
[tex]r=\sqrt{0.6^2+0.8^2}=1[/tex]
Substitute y =0.8, r=1 in the sine formula.
[tex]sin\theta=0.8[/tex]
We know that
[tex]csc\theta=\frac{1}{sin\theta}=\frac{1}{0.8}=1.25[/tex]
Consider the formula to find cosine.
[tex]cos\theta=\frac{x}{r}[/tex]
Substitute x =0.6 and r =1 in the equation.
[tex]cos\theta=0.6[/tex]
We know that
[tex]sec\theta=\frac{1}{cos\theta}=\frac{1}{0.6}=1.67[/tex]
Consider the formula to find cot.
[tex]cot\theta=\frac{x}{y}[/tex]
Substitute x =0.6 and y=0.8 in the equation.
[tex]cot\theta=\frac{0.6}{0.8}=0.75[/tex]
Final answer:
[tex]csc\theta=1.25[/tex][tex]sec\theta=1.67[/tex][tex]cot\theta=0.75[/tex]
