Question

find the exact values of the six trigonometric ratios of the angle $\theta$ in the triangle shown in the following figure. sin($\theta$) = cos($\theta$) = tan($\theta$) = csc($\theta$) = sec($\theta$) = cot($\theta$) =

Explanation:

Step1: Recall sine definition

$\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(\theta)=\frac{28}{100}=\frac{7}{25}$

Step2: Recall cosine definition

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(\theta)=\frac{96}{100}=\frac{24}{25}$

Step3: Recall tangent definition

$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(\theta)=\frac{28}{96}=\frac{7}{24}$

Step4: Recall cosecant definition

$\csc(\theta)=\frac{\text{hypotenuse}}{\text{opposite}}$
$\csc(\theta)=\frac{100}{28}=\frac{25}{7}$

Step5: Recall secant definition

$\sec(\theta)=\frac{\text{hypotenuse}}{\text{adjacent}}$
$\sec(\theta)=\frac{100}{96}=\frac{25}{24}$

Step6: Recall cotangent definition

$\cot(\theta)=\frac{\text{adjacent}}{\text{opposite}}$
$\cot(\theta)=\frac{96}{28}=\frac{24}{7}$

Answer:

$\sin(\theta)=\frac{7}{25}$
$\cos(\theta)=\frac{24}{25}$
$\tan(\theta)=\frac{7}{24}$
$\csc(\theta)=\frac{25}{7}$
$\sec(\theta)=\frac{25}{24}$
$\cot(\theta)=\frac{24}{7}$