Question

which shows the correct trig equation? sinθ = 8/18 cosθ = 18/8 tanθ = 8/18 tanθ = 18/8

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the side opposite to $\theta$ is $8$, and the side adjacent to $\theta$ is $18$.

Step2: Analyze each option

• For $\sin\theta=\frac{8}{18}$: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, but we don't know the hypotenuse. So this is incorrect.
• For $\cos\theta=\frac{18}{8}$: $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\frac{18}{8}>1$ (since hypotenuse $> $ adjacent in a right - triangle, $\cos\theta<1$). So this is incorrect.
• For $\tan\theta=\frac{8}{18}$: $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{8}{18}$. This is correct.
• For $\tan\theta=\frac{18}{8}$: $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, but here it should be $\frac{8}{18}$ (opposite $ = 8$, adjacent $=18$). So this is incorrect.

Answer:

$\tan\theta=\frac{8}{18}$ (the green option)