Flashcard #4: Trigonometric Ratios

Front

What is the definition of cosine in a right triangle?

Back

Cosine (Cos) is defined as 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 sine in a right triangle?

Back

Sine (Sin) is defined as 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 tangent in a right triangle?

Back

Tangent (Tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side. Formula: Tan X = Opp/Adj.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a^2 + b^2 = c^2.

Front

If Cos X = 15/17, what is the value of Sin X?

Back

Using the Pythagorean identity, Sin^2 X + Cos^2 X = 1, we find that Sin X = 8/17.

Front

What is the relationship between sine and cosine?

Back

Sine and cosine are co-functions: Sin X = Cos(90° - X) and Cos X = Sin(90° - X).

Front

What is the value of Tan X if Cos X = 15/17 and Sin X = 8/17?

Back

Tan X = Sin X / Cos X = (8/17) / (15/17) = 8/15.

Front

What is the sine of angle C if Cos C = 40/41?

Back

Using the Pythagorean identity, Sin^2 C + Cos^2 C = 1, we find that Sin C = 9/41.

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The hypotenuse can be found using the Pythagorean theorem: Hypotenuse = √(Opp^2 + Adj^2).

Front

What is the cosine of angle A if the adjacent side is 24 and the hypotenuse is 40?

Back

Cos A = Adj/Hyp = 24/40 = 3/5.