Question

which shows the correct trig equation?
cos 20 = 5/12
cos 5 = 20/12
sin 12 = 20/5
tan 20 = 5/12

Explanation:

Step1: Recall trigonometric ratios

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 with \(\theta = 20^{\circ}\), the adjacent side to the \(20^{\circ}\) angle is \(5\) and the hypotenuse is \(12\)

Step2: Check each option

• For \(\cos20=\frac{5}{12}\): Using the formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), with \(\theta = 20^{\circ}\), adjacent \(=5\) and hypotenuse \(=12\), so \(\cos20=\frac{5}{12}\) is correct.
• For \(\cos5=\frac{20}{12}\): The angle in the cosine function should be \(20^{\circ}\) (not \(5\)), so this is wrong.
• For \(\sin12=\frac{20}{5}\): The angle in the sine function is misused (should be \(20^{\circ}\)), and also \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), here the values are incorrect.
• For \(\tan20=\frac{5}{12}\): Using \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), the opposite side to \(20^{\circ}\) is not \(5\) (the adjacent is \(5\)), so this is wrong.

Answer:

\(\cos20 = 5/12\) (the orange option)