COLLEGE Geo Unit 9.4-9.5 Sin/Cos/Tan/Special triangles

Front

What is the sine function in a right triangle?

Back

The sine function (sin) is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine function in a right triangle?

Back

The cosine function (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the tangent function in a right triangle?

Back

The tangent function (tan) is the ratio of the length of the opposite side to the length of the adjacent side.

Front

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

Back

sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ).

Front

What is a special triangle?

Back

Special triangles are triangles with specific angle measures, such as 30-60-90 and 45-45-90 triangles, which have known side ratios.

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side opposite the 30° angle is x, the side opposite the 60° angle is x√3, and the hypotenuse is 2x.

Front

What are the side ratios of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, both legs are of equal length x, and the hypotenuse is x√2.

Front

How do you find the height of an object using trigonometry?

Back

Use the formula: height = distance from the object * tan(angle of elevation).

Front

What is the formula to find the length of a side in a right triangle using sine?

Back

If you know the angle and the hypotenuse, use: opposite side = hypotenuse * sin(angle).

Front

What is the formula to find the length of a side in a right triangle using cosine?

Back

If you know the angle and the hypotenuse, use: adjacent side = hypotenuse * cos(angle).