Question

question 6/9
which of the following trigonometric equations is valid for the side measurement x inches, diagonal measurement y inches, and angle measurement β° in the rectangle shown above?
a ( cos \beta^{circ}=\frac{x}{y} )
b ( cos \beta^{circ}=\frac{y}{x} )
c ( sin \beta^{circ}=\frac{x}{y} )
d ( sin \beta^{circ}=\frac{y}{x} )
e ( \tan \beta^{circ}=\frac{x}{y} )

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Identify the sides in the right - triangle

For the angle \(\beta^{\circ}\), the adjacent side to \(\beta^{\circ}\) is \(x\) (side of the rectangle) and the hypotenuse is \(y\) (diagonal of the rectangle).
So, \(\cos\beta^{\circ}=\frac{x}{y}\)

Answer:

A. \(\cos\beta^{\circ}=\frac{x}{y}\)