Trigonometric Ratios

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. Formula: sin(θ) = Opp/Hyp.

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. Formula: cos(θ) = Adj/Hyp.

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. Formula: tan(θ) = Opp/Adj.

Front

What is the mnemonic to remember trigonometric ratios?

Back

Soh Cah Toa: Sine = Opp/Hyp, Cosine = Adj/Hyp, Tangent = Opp/Adj.

Front

If the opposite side is 8 and the hypotenuse is 10, what is the sine of the angle?

Back

sin(θ) = Opp/Hyp = 8/10 = 0.8.

Front

If the adjacent side is 6 and the hypotenuse is 10, what is the cosine of the angle?

Back

cos(θ) = Adj/Hyp = 6/10 = 0.6.

Front

If the opposite side is 4 and the adjacent side is 3, what is the tangent of the angle?

Back

tan(θ) = Opp/Adj = 4/3.

Front

What is the Pythagorean theorem?

Back

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

Front

Find the missing side if one side is 3 and the hypotenuse is 5.

Back

Using the Pythagorean theorem: 3² + b² = 5²; b² = 25 - 9; b = 4.

Front

What is the sine of a 30-degree angle?

Back

sin(30°) = 1/2.