Question

1 matching 20 points given the following, match the trig function to its correct ratio: 17 8 15 15/8 15/17 17/15 8/17 8/15 17/8 tanθ = sinθ = cosθ =

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\)
For angle \(\theta\), the opposite side is \(8\), the adjacent side is \(15\), and the hypotenuse is \(17\)

Step2: Calculate \(\tan\theta\)

\(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{8}{15}\)

Step3: Calculate \(\sin\theta\)

\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{8}{17}\)

Step4: Calculate \(\cos\theta\)

\(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{15}{17}\)

Answer:

\(\tan\theta=\frac{8}{15}\), \(\sin\theta=\frac{8}{17}\), \(\cos\theta=\frac{15}{17}\)