1. Right Triangle Trigonometry
Advanced Math 6.2

2. Right triangle 0 < q < 90 Six trig ratios q hypotenuse
Side opposite to q q
Side adjacent to q
Advanced Math 6.2

3. Example Find the 6 trig functions of the triangle q 13 12 5
Advanced Math 6.2

4. If given the angle Make a triangle Make the short side 1
Two common triangles
45°- 45°- 90°
30°- 60°- 90°
Advanced Math 6.2

5. 45°- 45°- 90° triangle From geometry From Pythagorean thrm.
The two sides opposite equal angles are equal lengths
45° 1
From Pythagorean thrm.
hyp is
45° 1
Find sin, cos, and tan of 45°
Advanced Math 6.2

6. 30°- 60°- 90° triangle Half of an equilateral triangle2
From Pythagorean thrm.
opp is
60° 1 1
Find sin, cos, and tan of 30° and 60°
Advanced Math 6.2

7. Cofunctions Cofunctions of complementary angles are = sin and cos
tan and cot
sec and csc
Cofunctions of complementary angles are =
Advanced Math 6.2

8. You try
Find sin, cos, and tan of p/3 radians.
Advanced Math 6.2

9. Special angles
Chart on page 462
Advanced Math 6.2

10. TRIG IDENTITIES Reciprocal Identities Quotient Identities
Pythagorean Identities
Note
Advanced Math 6.2

11. SOH CAH TOA
Advanced Math 6.2

12. Examples If tan q = 5, find cot q cos q tan (90° - q) csc q
Advanced Math 6.2

13. Examples
Use trig identities to show that
Advanced Math 6.2

14. Using the calculator for trig functions
Check the mode
Only buttons for sin, cos, and tan
May need reciprocal identities
Advanced Math 6.2

15. Examples
Evaluate the following using a calculator. Round to three decimal places.
sin 16.35°
csc 16.35°
sec 0.75
cos 0.75
Advanced Math 6.2

16. Solving right triangles
45° r 20
Solve for r.
60° 18 y
Solve for y.
Advanced Math 6.2

17. Angles of elevation and depression
object
angle of elevation
observer
observer
angle of depression
object
Advanced Math 6.2

18. Example
A 10´ ladder leans against the side of a house. The ladder makes an angle of 60° with the ground. How far up the side of the house does the ladder reach?
Advanced Math 6.2