Trigonometry

Front

What is the definition of a hypotenuse in a right triangle?

Back

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

Front

How do you calculate the length of the hypotenuse using the Pythagorean theorem?

Back

The length of the hypotenuse can be calculated using the formula: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse: sin(θ) = opposite/hypotenuse.

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side: tan(θ) = opposite/adjacent.

Front

What is the relationship between sine, cosine, and tangent?

Back

The relationship can be expressed as: tan(θ) = sin(θ)/cos(θ).

Front

How do you find the length of the side opposite an angle using the sine ratio?

Back

To find the length of the opposite side, use the formula: opposite = hypotenuse × sin(θ).

Front

How do you find the length of the side adjacent to an angle using the cosine ratio?

Back

To find the length of the adjacent side, use the formula: adjacent = hypotenuse × cos(θ).

Front

What is the purpose of inverse trigonometric functions?

Back

Inverse trigonometric functions are used to find the angle when the lengths of the sides are known.

Front

How do you use the inverse sine function to find an angle?

Back

To find an angle using the inverse sine function, use the formula: θ = sin⁻¹(opposite/hypotenuse).