1. Trigonometric Identities
Lesson 14.4
Trigonometric Identities pp

2. Objective:
To prove trigonometric identities.

3. sec A = 1 cos csc A = 1 sin cot A = 1 tan
Three reciprocal ratios are multiplicative inverses of the sine, cosine, and tangent ratios.
sec A = 1
cos
csc A = 1
sin
cot A = 1
tan

4. Theorem 14.3
Sum of Squares Identity. For any angle x, sin2 x + cos2 x = 1.

5. EXAMPLE 1
Prove that tan x =
sin x
cos x

6. EXAMPLE 2
Prove that sin x sec x = tan x.

7. EXAMPLE 3
Prove that
(1 + cos x)(1 - cos x) = sin2 x.

8. General hints for proving identities:
1. Start with one side of the equation and transform it to the other side without working on both sides of the equation.
2. Work on the most complicated side first.
3. Use basic definitions and previously proven identities to simplify.

9. Homework pp

10. ►A. Exercises
Prove each identity.
5. cos x csc x = cot x

11. ►A. Exercises
Prove each identity.
7. cot2 x + 1 = csc2 x

12. ►A. Exercises
Prove each identity.
9. cot x + tan x = csc x sec x

13. 21. Any composite of two reflections across concurrent lines.
■ Cumulative Review
Match to each description the letter of the most specific term that applies.
21. Any composite of two reflections across concurrent lines.
translation
enlargement
isometry
reduction
E. reflection
F. rotation
G. similarity
H. transformation

14. 22. Any mapping with a scale factor greater than one
■ Cumulative Review
Match to each description the letter of the most specific term that applies.
22. Any mapping with a scale factor greater than one
translation
enlargement
isometry
reduction
E. reflection
F. rotation
G. similarity
H. transformation

15. 23. Any one-to-one correspondence from the plane onto the plane
■ Cumulative Review
Match to each description the letter of the most specific term that applies.
23. Any one-to-one correspondence from the plane onto the plane
translation
enlargement
isometry
reduction
E. reflection
F. rotation
G. similarity
H. transformation

16. 24. Any mapping that preserves distance
■ Cumulative Review
Match to each description the letter of the most specific term that applies.
24. Any mapping that preserves distance
translation
enlargement
isometry
reduction
E. reflection
F. rotation
G. similarity
H. transformation

17. 25. Any mapping that preserves shape
■ Cumulative Review
Match to each description the letter of the most specific term that applies.
25. Any mapping that preserves shape
translation
enlargement
isometry
reduction
E. reflection
F. rotation
G. similarity
H. transformation