Trigonometric Ratios and Angle Relationships

Front

What are the primary trigonometric ratios?

Back

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

Front

Define Sine (sin) in a right triangle.

Back

Sine is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

Define Cosine (cos) in a right triangle.

Back

Cosine is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

Define Tangent (tan) in a right triangle.

Back

Tangent is the ratio of the length of the opposite side to the length of the adjacent side.

Front

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

Back

sin(θ) = cos(90° - θ).

Front

What is the Pythagorean identity involving sine and cosine?

Back

sin²(θ) + cos²(θ) = 1.

Front

How do you find the missing angle in a right triangle if you know two sides?

Back

Use the inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) to find the angle.

Front

If sin(70°) = cos(?), what is the missing angle?

Back

20° (since sin(θ) = cos(90° - θ)).

Front

What is the value of tan(θ) if sin(θ) = 0.6 and cos(θ) = 0.8?

Back

tan(θ) = sin(θ) / cos(θ) = 0.6 / 0.8 = 0.75.

Front

What is the sine of a 30° angle?

Back

sin(30°) = 0.5.