Trigonometric Ratios

Front

What is the definition of a trigonometric ratio?

Back

A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. The primary trigonometric ratios are sine, cosine, and tangent.

Front

What is the formula for cosine (cos) in a right triangle?

Back

cos(θ) = adjacent side / hypotenuse.

Front

What is the formula for sine (sin) in a right triangle?

Back

sin(θ) = opposite side / hypotenuse.

Front

What is the formula for tangent (tan) in a right triangle?

Back

tan(θ) = opposite side / adjacent side.

Front

In a right triangle, if the hypotenuse is 10 and the adjacent side is 6, what is cos(θ)?

Back

cos(θ) = 6/10 = 0.6.

Front

In a right triangle, if the opposite side is 4 and the hypotenuse is 5, what is sin(θ)?

Back

sin(θ) = 4/5 = 0.8.

Front

In a right triangle, if the opposite side is 3 and the adjacent side is 4, what is tan(θ)?

Back

tan(θ) = 3/4 = 0.75.

Front

What is the hypotenuse in a triangle with sides of length 3 and 4?

Back

The hypotenuse is 5, calculated using the Pythagorean theorem: √(3² + 4²) = 5.

Front

What is the adjacent side of θ in a triangle where the hypotenuse is 13 and the opposite side is 5?

Back

The adjacent side can be found using the Pythagorean theorem: adjacent = √(13² - 5²) = 12.

Front

What is the relationship between sine and cosine?

Back

sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ).