Question

match the trig ratios

= \frac{\text{opposite}}{\text{hypotenuse}}

= \frac{\text{adjacent}}{\text{hypotenuse}}

= \frac{\text{opposite}}{\text{adjacent}}

Explanation:

🆕 New Concept Discovered: Trigonometric Ratios
Connecting right triangle sides to trig functions.

Step 1: Identify the ratio for Sine

The sine function (\(\sin\)) of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

$$ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} $$

Step 2: Identify the ratio for Cosine

The cosine function (\(\cos\)) of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

$$ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} $$

Step 3: Identify the ratio for Tangent

The tangent function (\(\tan\)) of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

$$ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} $$

A helpful memory aid for these relationships is the acronym SOH CAH TOA:

• Sine = Opposite / Hypotenuse
• Cosine = Adjacent / Hypotenuse
• Tangent = Opposite / Adjacent

Answer:

• sine (or \(\sin\)) \(= \frac{\text{opposite}}{\text{hypotenuse}}\)
• cosine (or \(\cos\)) \(= \frac{\text{adjacent}}{\text{hypotenuse}}\)
• tangent (or \(\tan\)) \(= \frac{\text{opposite}}{\text{adjacent}}\)