Question

Find the values of sin0, cos0, and tan0 for the given right triangle. Give exact values

Answer 1

`\sin (\theta)=(24)/(25),\cos (\theta)=(7)/(25)`

1) In this question, we can see a right triangle. So let's apply those trig ratios considering that the opposite leg to theta angle is 24, and the hypotenuse is 25 units long.

2) So we can write out:

`\begin{gathered} \sin (\theta)=(24)/(25) \\ \end{gathered}`

We need to find the adjacent leg to get the cosine of theta. Since this is a right triangle, we can make use of the Pythagorean Theorem to figure it out:

`\begin{gathered} a^2=b^2+c^2 \\ 25^2=24^2+c^2 \\ 625=576+c^2 \\ 625-576=576-576+c^2 \\ 49=c^2 \\ \sqrt[]{c^2}=\sqrt[]{49} \\ c=7 \end{gathered}`

3) So we can write the cosine as:

`\cos (\theta)=(7)/(25)`