Questions: The ratio of the side opposite θ to the hypotenuse represents which trigonometric function? Option #1: tan θ = (opposite) / (hypotenuse) Option #2: sin θ = (opposite) / (hypotenuse) Option #3: cos θ = (opposite) / (hypotenuse)

The ratio of the side opposite θ to the hypotenuse represents which trigonometric function?
Option #1: tan θ = (opposite) / (hypotenuse)
Option #2: sin θ = (opposite) / (hypotenuse)
Option #3: cos θ = (opposite) / (hypotenuse)

Transcript text: The ratio of the side opposite $\theta$ to the hypotenuse represents which trigonometric function? Option \#1: $\tan \theta=\frac{\text { opposite }}{\text { hypotenuse }}$ Option \#2: $\sin \theta=\frac{\text { opposite }}{\text { hypotenuse }}$ Option \#3: $\cos \theta=\frac{\text { opposite }}{\text { hypotenuse }}$

Solution

Solution Steps

Step 1: Identify the trigonometric function

The question asks which trigonometric function represents the ratio of the side opposite $\theta$ to the hypotenuse. Recall the definitions of the basic trigonometric functions:

$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$

Step 2: Compare with the given options

From the definitions above, the ratio of the side opposite $\theta$ to the hypotenuse corresponds to $\sin \theta$. Now, compare this with the given options:

Option \#1: $\tan \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ (Incorrect, as $\tan \theta$ involves the opposite and adjacent sides)
Option \#2: $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ (Correct)
Option \#3: $\cos \theta = \frac{\text{opposite}}{\text{hypotenuse}}$ (Incorrect, as $\cos \theta$ involves the adjacent and hypotenuse sides)