Question

which shows the correct trig equation? tanθ=14/8 cosθ=8/14 sinθ=8/14 cosθ=14/8

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).
For the given right - triangle, the hypotenuse \(c = 14\), the adjacent side to \(\theta\) is \(a=8\).

Step2: Calculate \(\cos\theta\)

Using the formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), we substitute the values. So \(\cos\theta=\frac{8}{14}\).
For \(\tan\theta\), if we assume the opposite side \(b=\sqrt{14^{2}-8^{2}}=\sqrt{196 - 64}=\sqrt{132}=2\sqrt{33}\), then \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}=\frac{2\sqrt{33}}{8}=\frac{\sqrt{33}}{4}
eq\frac{14}{8}\).
For \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{\sqrt{132}}{14}
eq\frac{8}{14}\). Also, \(\cos\theta=\frac{14}{8}>1\) is not possible since \(- 1\leqslant\cos\theta\leqslant1\)

Answer:

\(\cos\theta=\frac{8}{14}\) (the blue option)