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(X) = 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(X) = 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(X) = Opp/Adj.

Front

Calculate Sin(X) if Opposite = 27 and Hypotenuse = 45.

Back

Sin(X) = \frac{27}{45} = \frac{3}{5}.

Front

Calculate Cos(X) if Adjacent = 40 and Hypotenuse = 41.

Back

Cos(X) = \frac{40}{41}.

Front

Calculate Tan(X) if Opposite = 9 and Adjacent = 40.

Back

Tan(X) = \frac{9}{40}.

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: a^2 + b^2 = c^2.

Front

If Sin(X) = \frac{15}{17}, what is the value of Cos(X)?

Back

Using the Pythagorean identity, Cos(X) = \sqrt{1 - Sin^2(X)} = \sqrt{1 - \left(\frac{15}{17}\right)^2} = \frac{8}{17}.

Front

What is the relationship between the trigonometric ratios in a right triangle?

Back

The ratios are defined as follows: Sin(X) = Opp/Hyp, Cos(X) = Adj/Hyp, Tan(X) = Opp/Adj.

Front

What is the value of Tan(X) if Sin(X) = \frac{3}{5} and Cos(X) = \frac{4}{5}?

Back

Tan(X) = \frac{Sin(X)}{Cos(X)} = \frac{3/5}{4/5} = \frac{3}{4}.