Unit 7: Using Trig Function

Front

What is the definition of a trigonometric function?

Back

A trigonometric function relates the angles of a triangle to the lengths of its sides. The primary functions are sine, cosine, and tangent.

Front

What is the sine function?

Back

The sine function (sin) is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

Front

What is the cosine function?

Back

The cosine function (cos) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

Front

What is the tangent function?

Back

The tangent function (tan) is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

Front

How do you find the length of a side in a right triangle using trigonometric functions?

Back

You can use the sine, cosine, or tangent functions depending on the known angles and sides. For example, if you know an angle and the hypotenuse, use sine or cosine.

Front

What is the formula to find the angle using the sine function?

Back

The angle can be found using the inverse sine function: angle = sin^(-1)(opposite/hypotenuse).

Front

What is the formula to find the angle using the cosine function?

Back

The angle can be found using the inverse cosine function: angle = cos^(-1)(adjacent/hypotenuse).

Front

What is the formula to find the angle using the tangent function?

Back

The angle can be found using the inverse tangent function: angle = tan^(-1)(opposite/adjacent).

Front

If a slide is 10 ft high and declines at 43 degrees, how do you find the length of the slide?

Back

Use the sine function: sin(43) = opposite/hypotenuse. Rearranging gives hypotenuse = opposite/sin(43). Plug in 10 ft for opposite.

Front

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

Back

The lengths of the sides are proportional to the sine, cosine, and tangent of the angles.