REVIEW for BENCHMARK 12.16.24

Front

What is the formula to find the length of a bold arc in a circle?

Back

The length of a bold arc can be calculated using the formula: \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

Define cosine in terms of a right triangle.

Back

In a right triangle, the cosine of an angle \( A \) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: \( \cos A = \frac{\text{adjacent}}{\text{hypotenuse}} \).

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

How do you identify the opposite side in a right triangle?

Back

The opposite side is the side that is opposite to the angle you are considering in a right triangle.

Front

What is the sine function in relation to a right triangle?

Back

In a right triangle, the sine of an angle \( A \) is defined as the ratio of the length of the opposite side to the length of the hypotenuse: \( \sin A = \frac{\text{opposite}}{\text{hypotenuse}} \).

Front

If \( \sin X = \frac{16}{34} \), how can you find the angle \( X \)?

Back

To find the angle \( X \), use the inverse sine function: \( X = \sin^{-1}\left(\frac{16}{34}\right) \).

Front

What is the relationship between sine and cosine for complementary angles?

Back

For complementary angles, the sine of one angle is equal to the cosine of the other: \( \sin A = \cos(90 - A) \).

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

Front

How do you calculate the length of a side in a right triangle using trigonometric ratios?

Back

You can calculate the length of a side using the ratios: \( \sin A = \frac{\text{opposite}}{\text{hypotenuse}} \), \( \cos A = \frac{\text{adjacent}}{\text{hypotenuse}} \), and \( \tan A = \frac{\text{opposite}}{\text{adjacent}} \).

Front

What is the value of \( \cos A \) if the adjacent side is 21 and the hypotenuse is 29?

Back

Using the cosine definition, \( \cos A = \frac{21}{29} \).