Question

express x and y in terms of trigonometric ratios of θ for the following figure. (express your answer in terms of θ only.)

Explanation:

Step1: Use tangent ratio

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan\theta=\frac{x}{7}$, so $x = 7\tan\theta$.

Step2: Use cosine ratio

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\cos\theta=\frac{7}{y}$, so $y=\frac{7}{\cos\theta}=7\sec\theta$.

Answer:

$x = 7\tan\theta$
$y = 7\sec\theta$