Lesson 3: 8-4: Trigonometry

1. What are the ratios for trig functions: sine, cosine, and tangent?
2. What is the relationship between the sine of an angle and the cosine of its complement?
3. How do you find the measure of an angle in a right triangle?

Trigonometry
Trigonometric Ratio
Sine
Cosine
Tangent
Inverse Sine
Inverse Cosine
Inverse Tangent

G.SRT.7
Explain and use the relationship between sine and cosine of complementary angles.

A ratio of the lengths of the sides of a right triangle is called a trigonometric ratio. The three most common trigonometric ratios are sine, cosine, and tangent. Trigonometric ratios are used to find missing measures of a right triangle. The inverse of each trigonometric ratio yields the angle measure.

The steepness of a hiking trail is often expressed as a percent of grade. The steepest part of Bright Angel Trail in the Grand Canyon National Park has about a 15.7% grade. This means that the trail rises or falls 15.7 feet over a horizontal distance of 100 ft. You can use trigonometric ratios to determine that this steepness is equivalent to an angle of about 9 degrees.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections by using the length of one side of a right triangle and one acute angle to find all of the other missing parts of the triangle.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.