Flashcard No. 7.1-7.2 in Geometry (Trigonometric Ratios )

Front

What are the three primary trigonometric ratios?

Back

Sine (sin), Cosine (cos), and Tangent (tan).

Front

Define Sine (sin) in terms of a right triangle.

Back

Sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

Define Cosine (cos) in terms of a right triangle.

Back

Cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

Define Tangent (tan) in terms of a right triangle.

Back

Tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

What is the Pythagorean theorem?

Back

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

Front

If sin(θ) = 0.5, what is θ in degrees?

Back

θ = 30°.

Front

If cos(θ) = 0.6, what is the length of the adjacent side if the hypotenuse is 10?

Back

Adjacent side = 0.6 * 10 = 6.

Front

If tan(θ) = 1, what is θ in degrees?

Back

θ = 45°.

Front

What is the relationship between the sine and cosine of complementary angles?

Back

sin(θ) = cos(90° - θ).

Front

Calculate the measure of angle X if sin(X) = 0.75. Round to the nearest hundredth.

Back

X ≈ 48.59°.