Geometry Trigonometry & Applications

Question 1

What does sine (sin) represent in a right triangle?

Accepted Answer

Opposite over hypotenuse

Answer

In a right-angled triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. This relationship is a fundamental part of trigonometry, often remembered by the "SOH" in SOH-CAH-TOA. It helps relate angles to side lengths.

Question 2

What does cosine (cos) represent in a right triangle?

Accepted Answer

Adjacent over hypotenuse

Answer

In a right-angled triangle, the cosine of an acute angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. This trigonometric ratio is a key component of SOH-CAH-TOA, specifically the "CAH" part. It is used to find unknown side lengths or angles.

Question 3

What does tangent (tan) represent in a right triangle?

Accepted Answer

Opposite over adjacent

Answer

In a right-angled triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. This ratio is represented by the "TOA" in the SOH-CAH-TOA mnemonic. It is particularly useful when the hypotenuse is not involved in the calculation.

Question 4

What is the Pythagorean identity?

Accepted Answer

sin²θ + cos²θ = 1

Answer

The Pythagorean identity, sin²θ + cos²θ = 1, is a fundamental trigonometric identity derived directly from the Pythagorean theorem and the definitions of sine and cosine in a right triangle. It holds true for any angle θ and is widely used to simplify trigonometric expressions and solve equations.

Question 5

Which function is used to find an angle given two sides?

Accepted Answer

Inverse functions like sin⁻¹

Answer

When you know the ratio of two sides in a right triangle (e.g., opposite/hypotenuse for sine), you use inverse trigonometric functions (arcsin, arccos, arctan) to find the measure of the angle itself. For example, if sin(θ) = 0.5, then θ = sin⁻¹(0.5) = 30 degrees. These functions essentially "undo" the regular trigonometric functions.

Geometry Practice Test

Geometry Practice Test

Geometry Trigonometry & Applications