Question

Find the values of sin 0, cos 0, and tan e for the given right triangle. Give the exact values.sin e11cos e =tan =512

Answer 1

ANSWER:

$\begin{gathered} \sin \theta=\frac{5}{13} \\ \cos \theta=\frac{12}{13} \\ \tan \theta=\frac{5}{12} \end{gathered}$

STEP-BY-STEP EXPLANATION:

We must calculate all the sides of the triangle in order to determine the trigonometric ratios. The longest side of the triangle is the hypotenuse and we calculate it using the Pythagorean theorem:

$\begin{gathered} c^2=a^2+b^2 \\ \text{ In this case:} \\ c^2=12^2+5^2 \\ c=\sqrt{144+25} \\ c=\sqrt[]{169} \\ c=13 \end{gathered}$

Now, we calculate each trigonometric ratio:

$\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{13} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{12}{13} \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{5}{12} \end{gathered}$