Name_________________ Test Date_____________ Got It Needs More Practice Extra Practice 3
and 180o  β  270o . 5
- 34
Solution: cscβ =
5
2. Verify: tanx  cscx=secx sinx 1


Solution:
cosx sin x
1
 sec x cos x
2
1  sin 
3. Verify:
 cot 2  2
sin 
cos 2
Solution:
 cot 2
2
sin

Only work on ONE side until it matches the other side.
Suggestions:  Work on the most complicated side.  Substitute one or more trig identities to simplify.  Look to replace with Pythagorean Identities.  Get a common denominator to add or subtract.  Write in terms of sine and cosine.  Factor as necessary.  Multiply if necessary.  Split into 2 or more fractions.  FOIL  Multiply by the conjugate.  Multiply by “1.”  Combine like terms.  Reduce.  Work backwards if you get stuck. See Notes, HW, and quizzes for samples.
sin( A  B )  sin A cos B  cos A sin B
See Notes and HW #1 See Notes and HW #s 2, 3, 4, 9 and opener #5 Also see quizzes. Honors AA w/Trig
Chapter 14—Trig Identities Target Goal Self Assessment Directions: Complete this sheet by reading the target goals, studying the samples, and checking off the boxes so you know what you need to practice for the test. Target Goals Samples
The students will be able to: 14.1 (HW #1) 
use and memorize reciprocal identities to find trigonometric values and to simplify expressions and verify equations.  use and memorize quotient identities to find trigonometric values and to simplify expressions and verify equations.  use and memorize Pythagorean identities (9 variations) to find trigonometric values and to simplify expressions and verify equations.  use trigonometric identities to simplify expressions . 14.2 (HW #s 2,3,4)  verify trigonometric identities by transforming one side of an equation into the form of the other side. 14.3 (HW #5)  use and memorize sum and difference identities to find trigonometric values and to simplify expressions. See next page for more. 1. Find the cscβ if cotβ=
4. Write from memory the 9 Pythagorean, 6 reciprocal, and 2 quotient identities. sin( A  B )  sin A cos B  cos A sin B
cos( A  B )  cos A cos B  sin A sin B
cos( A  B )  cos A cos B  sin A sin B
See next page for samples. See Notes and HW # 5 and opener #6  verify trigonometric identities by using sum and difference identities. 1. Find: cos(270+ )
Solution: sin
2. Find: sin(270+ )
Solution: -cos
o
3. Find the exact value for sin 15 . Solution:
 19
 12
3. Find the exact value for cos 
6 2
4
6 2
4

 . Solution:

o
5. Verify: cos(180 - )  -cos
Solution : cos180 cos   sin 180 sin  
-1(cos )+0(sin ) 
-cos =
14.4 (HW #6) sin 2  2sin  cos 
 use and memorize cos 2  cos 2   sin 2 
double‐angle identities 2
for sine and cosine to find cos 2  1  2sin 
trigonometric values and cos 2  2 cos 2   1
to simplify expressions. Sample:
See Notes and HW #6 and opener #7 1
Suppose x is in the fourth quadrant and sinx = - .
8 Find cos2x and sin2x.
Solution : cos 2 x 
14.5 (HW #7 and #8)  solve trigonometric equations.  find extraneous solutions from trigonometric equations. Samples:
1. Solve: sin 2  cos 2  cos   0 if 0o   <360o
Solution :   0o ,90o , 270o
2. Solve: 4sin 2  1 if 0o   <360o
Solution :   30 ,150 , 210 ,330
o
o
o
o
See Notes and HW #7 and opener #8 3. Solve: 2sin 2  3sin   2  0 if 0   <2
Solution :  
31
-3 7
; sin 2 x 
32
32
 5
,
6 6
Test Break Down: 36 problems—100 total points—NO partial credit!! 17 Identities—Matching—1 point each—NO partial credit 8 Identities—Write them out—1 point each—NO partial credit 4 Verify—8 point each—NO partial credit 2 problems to find the exact answer using sum or difference identities—5 points each—NO partial credit. 2 problems to find the cos 2x and the sin 2x—6 points each—NO partial credit. 3 trig equations to solve—7 points each—NO partial credit. 3 extra credit problems—2 points each—w/answers circled—NO partial credit. Extra Practice: HW #9 Worksheet (optional—solutions on line) Reference your corrected opener/notes, quizzes, and homework from chapter 14.
Also reference the #9 review packet and the extra practice packet. Use your “foldable” as a study guide.