Chapter 5Trigonometric Functions

Section 5.2Trigonometric Functions of Acute Angles

Trigonometric Functions of Acute Angles

When working with right triangles, it is convenient to refer to the side opposite an angle or the side adjacent to (next to) an angle.

Trigonometric Functions of Acute Angles

Consider an angle q in the right triangle shown below. Let x and y represent the lengths, respectively, of the adjacent and opposite side of the triangle, and let r be the length of the hypotenuse. Six possible ratios can be formed:

Trigonometric Functions of Acute Angles

sin q = csc q =

cos q = sec q =

tan q = cot q =

Trigonometric Functions of Acute Angles

Example 1

Find the six trigonometric functions of q for the triangle given in the Figure 5.32 below.

Example 2

Given that q is and acute angle andcos q = , find tan q.

Trigonometric Functions of Special Angles

Special Angles

Trigonometric Functions of Special Angles

Example

Find the exact value of sin2450 + cos2600.

Reciprocal Functions

sin q = cos q =

tan q = sec q =

csc q = cot q =

Applications

From a point 115 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 64.30. Find the height of the tree to the nearest foot.

Applications

If the distance from a plane to a radar station is 160 miles and the angle of depression is 330, find the number of ground miles from a point directly below the plan to the radar station.

Applications

The angle of elevation from point A to the top of a space shuttle is 27.20. From a point 17.5 meters further from the space shuttle, the angle of elevation is 23.90. Find the height of the space shuttle.

Assignment

Section 5.2 - Worksheet