1. Splash Screen

2. Five-Minute Check (over Chapter 13) Then/Now New Vocabulary
Key Concept: Basic Trigonometric Identities
Example 1: Use Trigonometric Identities
Example 2: Simplify an Expression
Example 3: Real-World Example: Simplify and Use an Expression
Lesson Menu

3. Rewrite 240° in radians. A. B. C. D. A B C D
5-Minute Check 1

4. A B C D Find the exact value of tan (–120°). A. B. C. D.
5-Minute Check 2

5. Solve ΔABC shown. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
A. c = 5.3, A = 26°, B = 118°
B. c = 5.3, A = 118°, B = 26°
C. c = 6, A = 26°, B = 118°
D. c = 6, A = 118°, B = 26° A B C D
5-Minute Check 3

6. Georgia is watching a space shuttle lift off from 0. 5 mile away
Georgia is watching a space shuttle lift off from 0.5 mile away. When she looks up at the shuttle at a 60° angle, how high is the space shuttle?
A mi
B mi
C mi
D mi A B C D
5-Minute Check 4

7. A B C D Find the amplitude and period of y = 2 cos A. 2 B. 2; 4
5-Minute Check 5

8. Which measure is needed to solve ΔABC using the Law of Cosines?
A. side a
B. side b
C. angle B
D. angle C A B C D
5-Minute Check 6

9. You evaluated trigonometric functions. (Lesson 13–7)
Use trigonometric identities to find trigonometric values.
Use trigonometric identities to simplify expressions.
Then/Now

10. trigonometric identity
Vocabulary

11. Concept

12. A. Find tan  if sec  = –2 and 180 <  < 270.
Use Trigonometric Identities
A. Find tan  if sec  = –2 and 180 <  < 270.
tan2 + 1 = sec2 Trigonometric identity
tan2 = sec2 – 1 Subtract 1 from each side.
tan2 = (–2)2 – 1 Substitute –2 for sec .
tan2 = 4 – 1 Square –2.
tan2 = 3 Subtract.
Take the square root of each side.
Answer: Since  is in the third quadrant, tan  is positive. Thus, tan θ =
Example 1A

13. sin2 + cos2 = 1 Trigonometric identity
Use Trigonometric Identities B.
sin2 + cos2 = 1 Trigonometric identity
Subtract.
Take the square root of each side.
Example 1B

14. Answer: Since  is in the second quadrant, sin  is positive. Thus, .
Use Trigonometric Identities
Answer: Since  is in the second quadrant, sin  is positive. Thus,
Example 1B

15. A. B. C. D. A B C D
Example 1A

16. A. 5 B. C. D. A B C D
Example 1B

17. Simplify sin  (csc  – sin  ).
Simplify an Expression
Simplify sin  (csc  – sin  ).
Distributive Property
= 1 – sin2  Simplify.
= cos2  1 – sin2  = cos2 
Answer: cos2 
Example 2

18. Simplify tan  cot .
A. –1
B. 0
C. 1
D. –2 A B C D
Example 2

19. Simplify and Use an Expression
A. LIGHTING The amount of light that a source provides to a surface is called the illuminance. The illuminance E in foot candles on a surface is related to the distance R in feet from the light source. The formula where I is the intensity of the light source measured in candles and θ is the angle between the light beam and a line perpendicular to the surface, can be used in situations in which lighting is important, as in photography. Solve the illuminance formula in terms of R.
Example 3A

20. Multiply each side by ER2.
Simplify and Use an Expression
Original equation
Multiply each side by ER2.
Divide each side by E.
Example 3A

21. Multiply each side by cos .
Simplify and Use an Expression
Multiply each side by cos .
Take the square root of each side.
Answer:
Example 3A

22. B. Is the equation in part A equivalent to
Simplify and Use an Expression
B. Is the equation in part A equivalent to
Original equation
Cross products
Divide each side by E.
Example 3B

23. Take the square root of each side.
Simplify and Use an Expression
Take the square root of each side.
Answer:
Example 3B

24. A. Solve the formula A. B. C. D. A B C D
Example 3A

25. B. Is the equation equivalent to ?
A. yes
B. no A B
Example 3

26. End of the Lesson