Finding Sides and Angles using Trigonometry

Front

What is the primary purpose of trigonometry in solving triangles?

Back

To find unknown sides and angles in right triangles using the relationships between the angles and sides.

Front

Define the sine function in terms of a right triangle.

Back

Sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse (sin(θ) = O/H).

Front

What is the cosine function in terms of a right triangle?

Back

Cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse (cos(θ) = A/H).

Front

Define the tangent function in terms of a right triangle.

Back

Tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side (tan(θ) = O/A).

Front

What is the Pythagorean theorem and how is it used in trigonometry?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²). It is used to find the length of a side when the lengths of the other two sides are known.

Front

How do you find the length of a side using the sine function?

Back

To find the length of a side using sine, use the formula: O = H * sin(θ), where O is the opposite side, H is the hypotenuse, and θ is the angle.

Front

How do you find the length of a side using the cosine function?

Back

To find the length of a side using cosine, use the formula: A = H * cos(θ), where A is the adjacent side, H is the hypotenuse, and θ is the angle.

Front

How do you find the length of a side using the tangent function?

Back

To find the length of a side using tangent, use the formula: O = A * tan(θ), where O is the opposite side, A is the adjacent side, and θ is the angle.

Front

What is the relationship between the angles and sides in a right triangle?

Back

The angles in a right triangle determine the ratios of the lengths of the sides, which can be expressed using sine, cosine, and tangent functions.

Front

How can you determine an unknown angle in a right triangle?

Back

To determine an unknown angle, use the inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹, depending on the known sides.