1. 4.3 Right Triangle Trigonometry
Objectives:
Evaluate trigonometric functions of acute angles
Use the fundamental trigonometric identities
Use trigonometric functions to model and solve real-life problems

2. Trigonometric Functions
Given a right triangle with acute angle 
hyp
opp 
adj
Precalculus
4.3 Right Triangle Trigonometry

3. 4.3 Right Triangle Trigonometry
Example 1
Evaluate the six trig functions of the angle  shown in the right triangle
sin  =
cos  =
tan  =
csc  =
sec  =
cot  = 5 12 13 
Precalculus
4.3 Right Triangle Trigonometry

4. 4.3 Right Triangle Trigonometry
Example 2
Find the value of x for the right triangle shown x 15
30°
Precalculus
4.3 Right Triangle Trigonometry

5. 4.3 Right Triangle Trigonometry
Example 3
Solve ∆ABC A B C
62° 6 c b
Precalculus
4.3 Right Triangle Trigonometry

6. 4.3 Right Triangle Trigonometry
You Try
Solve ∆ABC A B C
30° a c
Precalculus
4.3 Right Triangle Trigonometry

7. Special Triangles 30º-60°-90°
Recall the conversions
30°= 60°=
60° 2 1
30°
Precalculus
4.3 Right Triangle Trigonometry

8. Special Triangles 45º-45°-90°
Recall the conversion
45°=
45° 1
45° 1
Precalculus
4.3 Right Triangle Trigonometry

9. Co-functions of Complementary Angles
Look back at the sines and cosines for the triangle
Note that sin 30°=cos 60°
Co-functions of complementary angles are equivalent
Precalculus
4.3 Right Triangle Trigonometry

10. Trigonometric Identities
Reciprocal Identities
Precalculus
4.3 Right Triangle Trigonometry

11. Trigonometric Identities
Quotient Identities
Precalculus
4.3 Right Triangle Trigonometry

12. Trigonometric Identities
Pythagorean Identities
Note: sin2 is (sin )2 not sin (2)
Precalculus
4.3 Right Triangle Trigonometry

13. 4.3 Right Triangle Trigonometry
Example 4
Given sin=0.6, find the value of cos
Given sin=0.6, find the value of tan
Precalculus
4.3 Right Triangle Trigonometry

14. 4.3 Right Triangle Trigonometry
Example 5
Use trigonometric identities to transform one side of the equation into the other.
cossec=1
(sec+tan)(sec-tan)=1
Precalculus
4.3 Right Triangle Trigonometry

15. 4.3 Right Triangle Trigonometry
Surveying
A surveyor is standing 50 ft from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?
Precalculus
4.3 Right Triangle Trigonometry

16. 4.3 Right Triangle Trigonometry
River Walk
You are 200 yards from a river. Rather than walking directly to the river, you walk 400 yards along a straight path to the river’s edge. Find the acute angle ө between this path and the river’s edge.
Precalculus
4.3 Right Triangle Trigonometry

17. 4.3 Right Triangle Trigonometry
Skateboarding
Find the length c of the skateboard ramp.
Precalculus
4.3 Right Triangle Trigonometry

18. 4.3 Right Triangle Trigonometry
Homework
Star Wars Worksheet
Page 285
44-54 even, all
Precalculus
4.3 Right Triangle Trigonometry