Sec 6.2 Trigonometry of Right Triangles

Objectives:•To define and use the six trigonometric functions as ratios of sides of right triangles.•To review special right triangles.•To solve right triangles using trigonometric ratios.

Trigonometric Ratios

opposite adjacent oppositesin cos tan

hypotenuse hypotenuse adjacent

hypotenuse hypotenuse adjacentcsc sec cot

opposite adjacent opposite

Ex 1. Find the six trig ratios of the angle .

Ex 2. Sketch a right triangle with acute angle and find the other five trig ratios of .

a) b) 3cos

4

13csc

12

Class Work

1. Find the six trig ratios of the angle .

2. a) Find sin and cos

b) Find tan and cot

c) Find sec and csc

7

6

7

4

3. Sketch a right triangle with acute angle and find the other five trig ratios of .

a) b) 7

cos8

tan 3

Special Triangles

1

12

45

45 30

601

23

in degrees

in radians sin cos tan csc sec cot

30

45

60

Ex 3. Evaluate the following without a calculator.

a) b) sin cos3 3

cos60 sec60

Ex 4. Find the exact value of x.

a) b) x

13 45

60x

21

Class Work

Evaluate the expression without using a calculator.4. sin 30 csc 30

5. 2

sin cos sin cos3 6 6 3

Find the exact value of x.

6. 7.

Solving a Right Triangle

• A triangle has six parts—three angles and three sides.

• To solve a triangle means to determine all of its parts from the information known about the triangle.– In other words, we determine the lengths

of the three sides and the measures of the three angles.

Ex 5. Solve the triangle.

a) b)

Class Work

Solve the triangle.8. 9.

10. From the top of a 200 ft lighthouse, the angle of depression to a ship in the ocean is 23. How far is the ship from the base of the lighthouse?

HW #2 p484 1-35 odd, 49, 50.