Question

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

Explanation:

Step1: Recall trigonometric ratios

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

Step2: Check 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 \(\tan\theta=\frac{8}{18}\): Since \(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\) and opposite \( = 8\), adjacent \(=18\), this is correct.
• For \(\tan\theta=\frac{18}{8}\): Opposite is \(8\) and adjacent is \(18\), so \(\tan\theta=\frac{8}{18}

eq\frac{18}{8}\). This is incorrect.

• For \(\cos\theta=\frac{18}{8}\): \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), and adjacent \( = 18\), but also \(\frac{18}{8}>1\) (since cosine of an angle \(\theta\in[0,\frac{\pi}{2}]\) in a right - triangle has \(\cos\theta\in[0,1]\)). This is incorrect.

Answer:

\(\tan\theta = 8/18\) (the option in the blue box)