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Chapter 7 – Pre-Calc Review
7.1 Inverse sine, cosine and tangent functions
Find the exact value.
2
1. Cos(cos-1 (- ) )
2. sin(sin-1 2.3)
3
3. sin-1(sin
7
)
6
4. Find the inverse, f-1(x), of the function, f(x) and state the domain and range of f(x) and
f-1(x). f(x) = cos(x+2) + 1
7.2 More inverse trigonometric functions
Find the exact value.
1
1
5. sin(cos-1 ( ) )
6. tan(cos-1 )
2
3
Use a calculator to find the value.
1
8. csc-1(5)
9. cot-1 (  )
2
7. cos(tan-1u)
7.3 Trigonometric Identities
Establish the identity
csc v  1 1  sin v
cos   sin   sin 3 

10.
11.
 cot   cos 2 
csc v  1 1  sin v
sin 
12. (tan + tan)(1-cot cot) + (cot + cot)(1-tantan)=0
7.4 Sum and Difference Formulas
Find the exact value.
7
13. tan (
)
14. cos(105)
12
15. tan(
19
)
12
Establish the identity
cos(   )
16.
 cot   tan 
sin  cos 
Find the exact value
4
12
17.cos(tan-1 ( ) + cos-1( ))
3
13
18. sec(tan-1u + cos-1 v)
7.5 Double-angle and half-angle formulas
Find the exact value
19. cos(22.5)
20. csc(
7
)
8
Establish the identity
21. (4sinucosu)(1-2sin2u) = sin(4u)
7.7 Trigonometric Equations
Give the general form for all solutions
3
22. cos = 
2
23. cot  2   1
24. sin(2) = -1
Solve on interval [0,2π)
25. 4cos2 - 3 = 0
7.8 More Equations
Solve on the interval, 0 ≤  ≤ 2π.
26. cos2 – sin2 + sin = 0
27. cos(2) + 5cos + 3 = 0
28. sin + cos = -
29. 4cos(3x) – ex = 1, x > 0 (use graphing calc)

2
3
2 2
7.
Answer box: 1.
5.
3
2
6.
2.not defined 3.
1
1 u2
2

6

4. f-1(x) = cos-1( x-1) -2 f(x): domain: all Reals, range: 0 ≤ y ≤ 2. f-1(x): domain: 0 ≤ x ≤ 2, range: -2 ≤ y ≤ π - 2.
8. 0.20 9. 2.03 10. multiply each term by sin v 11. a) Factor out sin on top. b) split the fraction c) change cos/sin to cot and
1-sin2 to cos2. 12. a) multiply binomials b) cancel all tan times cot with the same angle c) positive and negative terms cancel each other out. 13. -2 14.
1
( 2  6)
4
sin/cos = tan. 17.
16
65
15.
18.
2  3
16. a) expand the difference formula b) split up the fraction c) cos cancel and cos/sin = cot, then sin cancels and
1 u2
v  u 1  v2
2 2
2
19.
2
20.
2 2
now it’s the double angle formula for 2u for sin, so its sin(4u).
5
7
 2k ,  
 2k
6
6
2 4
,
27. {
}
3 3
5
28. {
} 29. 0.31
4
22.

3
23.

 5 9 13
8
,
8
,
8
,
8

24.

21. a) turn the 1st term into 2sin(2u) and the second one to cos(2u) b)
3
 k
4
25.
 5 7 11
6
,
6
,
6
,
6
26. {
 7 11
2
,
6
,
6
}