Trigonometry Review

Front

What is the definition of Sine in a right triangle?

Back

Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the definition of Cosine in a right triangle?

Back

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the definition of Tangent in a right triangle?

Back

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side.

Front

What is the Pythagorean Theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides: a² + b² = c².

Front

How do you find the length of a missing side using the Sine function?

Back

Use the formula: sin(θ) = opposite/hypotenuse. Rearrange to find the opposite side: opposite = hypotenuse * sin(θ).

Front

How do you find the length of a missing side using the Cosine function?

Back

Use the formula: cos(θ) = adjacent/hypotenuse. Rearrange to find the adjacent side: adjacent = hypotenuse * cos(θ).

Front

How do you find the length of a missing side using the Tangent function?

Back

Use the formula: tan(θ) = opposite/adjacent. Rearrange to find the opposite side: opposite = adjacent * tan(θ).

Front

If the hypotenuse is 10 cm and the angle is 30°, what is the length of the opposite side?

Back

Using sine: opposite = 10 * sin(30°) = 10 * 0.5 = 5 cm.

Front

If the hypotenuse is 10 cm and the angle is 60°, what is the length of the adjacent side?

Back

Using cosine: adjacent = 10 * cos(60°) = 10 * 0.5 = 5 cm.

Front

If the opposite side is 3 cm and the adjacent side is 4 cm, what is the angle using Tangent?

Back

tan(θ) = opposite/adjacent = 3/4. θ = arctan(3/4) ≈ 36.87°.