Basic Trig Ratios

Front

What is the definition of sine (sin) 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 (cos) 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 (tan) 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 does SOH-CAH-TOA stand for?

Back

SOH-CAH-TOA is a mnemonic to remember the definitions of sine, cosine, and tangent: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

Front

What is the formula to find the angle using sine?

Back

The angle can be found using the formula: Angle = arcsin(opposite/hypotenuse).

Front

What is the formula to find the angle using cosine?

Back

The angle can be found using the formula: Angle = arccos(adjacent/hypotenuse).

Front

What is the formula to find the angle using tangent?

Back

The angle can be found using the formula: Angle = arctan(opposite/adjacent).

Front

In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is sin(θ)?

Back

sin(θ) = opposite/hypotenuse = 3/5.

Front

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

Back

cos(θ) = adjacent/hypotenuse = 4/5.

Front

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

Back

tan(θ) = opposite/adjacent = 3/4.