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Sec 6.2 Trigonometry of Right Triangles

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Title: Sec 6.2 Trigonometry of Right Triangles Last modified by: tyoung Created Date: 1/29/2009 3:31:59 AM Document presentation format: On-screen Show – PowerPoint PPT presentation

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Title: Sec 6.2 Trigonometry of Right Triangles


1
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.

2
Trigonometric Ratios
3
Ex 1. Find the six trig ratios of the angle ?.
4
Ex 2. Sketch a right triangle with acute angle ?
and find the other five trig ratios of ?.
  • a) b)

5
Class Work
  • Find the six trig ratios of the angle ?.
  • a) Find sin ? and cos ?
  • b) Find tan ? and cot ?
  • c) Find sec ? and csc ?

6
  • 3. Sketch a right triangle with acute angle ?
    and find the other five trig ratios of ?.
  • a) b)

7
Special Triangles
? in degrees ? in radians sin ? cos ? tan ? csc ? sec ? cot ?
30?
45?
60?
8
Ex 3. Evaluate the following without a calculator.
  • a) b)

9
Ex 4. Find the exact value of x.
  • a) b)

10
Class Work
  • Evaluate the expression without using a
    calculator.
  • 4. sin 30? csc 30?
  • 5.

11
  • Find the exact value of x.
  • 6. 7.

12
Solving a Right Triangle
  • A triangle has six partsthree 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.

13
Ex 5. Solve the triangle.
  • a) b)

14
Class Work
  • Solve the triangle.
  • 8. 9.

15
  • 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?

16
  • HW 2 p484 1-35 odd, 49, 50.
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