Flashcard 9 Unit 5: Trigonometric Functions

Front

What is the definition of a trigonometric function?

Back

A trigonometric function relates the angles of a triangle to the lengths of its sides. The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan).

Front

What is the sine of an angle in a right triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. It is defined as: sinA = \frac{\text{opposite}}{\text{hypotenuse}}.

Front

What is the cosine of an angle in a right triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. It is defined as: cosA = \frac{\text{adjacent}}{\text{hypotenuse}}.

Front

What is the tangent of an angle in a right triangle?

Back

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. It is defined as: tanA = \frac{\text{opposite}}{\text{adjacent}}.

Front

How do you find the measure of an angle using the sine function?

Back

To find the measure of an angle using the sine function, use the inverse sine function: A = \sin^{-1}(\frac{\text{opposite}}{\text{hypotenuse}}).

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

Front

What is the relationship between sine and cosine?

Back

The sine and cosine functions are related by the identity: sin^2(A) + cos^2(A) = 1.

Front

What is the formula for finding the length of a side in a right triangle using trigonometric functions?

Back

To find the length of a side, use the formulas: \text{opposite} = \text{hypotenuse} \cdot \sin(A) and \text{adjacent} = \text{hypotenuse} \cdot \cos(A).

Front

How do you reduce a fraction in trigonometric ratios?

Back

To reduce a fraction in trigonometric ratios, divide the numerator and denominator by their greatest common divisor (GCD).

Front

What is the sine ratio for a 30-degree angle?

Back

The sine ratio for a 30-degree angle is: sin(30°) = \frac{1}{2}.