Question

which shows the correct trig equation?
cosθ=10/6
tanθ=10/6
tanθ=6/10
sinθ=6/10

Explanation:

Step1: Recall trigonometric ratios

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

Step2: Analyze each option

• For \(\cos\theta=\frac{10}{6}\): \(\cos\theta\) should be \(\frac{\text{adjacent}}{\text{hypotenuse}}\), and \(\frac{10}{6}> 1\) (since \(\cos\theta\leq1\)), so this is wrong.
• For \(\tan\theta=\frac{10}{6}\): \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), but the values are mis - placed.
• For \(\tan\theta=\frac{6}{10}\): \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), values are mis - placed.
• For \(\sin\theta=\frac{6}{10}\): Here, if we assume the side of length \(6\) is opposite to \(\theta\) and the hypotenuse is \(10\), then \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{6}{10}\) (by the definition of the sine function in a right - triangle).

Answer:

\(\sin\theta = 6/10\)