chapter 6 trig 1060. find an equation that completes the fundamental trigonometric identity....
TRANSCRIPT
Chapter 6Trig 1060
Find an equation that completes the
fundamental trigonometric identity. Sin(-x)=
csc
x
-sin
x
-csc
x
sin
x
0% 0%0%0%
1. csc x
2. -sin x
3. -csc x
4. sin x
Find the expression that completes the fundamental trigonometric identity.
tan
u
-tan
u
-cot
u
cot u
0% 0%0%0%
tan( )2
u1. tan u
2. -tan u
3. -cot u
4. cot u
Use trigonometric substitution to write the algebraic expression as a trigonometric function of
, . , secwhere x x02
7 28 22
* * * *
0% 0% 0%0%0%
2 7 tan4 7 sin2 7 2 cos
28 2tan
1. *
2. *
3. *
4. *
Factor the expression and use the fundamental identities to simplify
cos csc cos2 2 2x x x
* * * *
1
0% 0%0%0%
cos tan2 2x xcos2 xcos cot2 2x x
1. *
2. *
3. *
4. * 1
Use the given values to evaluate (If possible) the remaining trigonometric functions
• Sin x• Cos x• Sec x• Cot x
csc , tanx x 109
10
10
3
Find a fundamental identity that could be used to verify the identity given
Pyt
hagor
ean id
entit
y
Quot
ient i
dentit
y
Eve
n/odd
iden
tity
Cofu
nctio
n iden
tity
0% 0%0%0%
sin
cos
2
211
x
x
1. Pythagorean identity
2. Quotient identity
3. Even/odd identity
4. Cofunction identity
Find an expression to complete the identity
2 22sin cos
csc
x x
x
0% 0% 0%0%
1 sincos
x
x1. *
2. * sinx
3. *
4. * cos x
1 csccsc
x
x
Find an expression that completes the identity
-2 s
in x 0
Tan
x
2 +
cos
x
0% 0%0%0%
sin
cos
cos
sin
x
x
x
x1
1
1. -2 sin x
2. 0
3. Tan x
4. 2 + cos x
Find an expression to complete the identity
1. * 1
2. *
3. *
4. *
sin ( csc )2 21t t
* 1 * * *
0% 0%0%0%
sin4 tsin2 1t 1 2 sin t
Find the x-values that are solutions of the equation
1. *
2. *
3. *
4. *
5 15 02cot x
* * * *
0% 0%0%0%
4 2
2
3
5
6, , ,
3
2
3
4
3
5
3, , ,
4
3
4
5
4
7
4, , ,
6
5
6
7
6
11
6, , ,
Express sin9x-sin5x as a product containing only sines and/or cosines
-2si
n2xco
s7x
-2si
n7xco
s2x
2si
n7xc
os2x
2si
n2xc
os7x
0% 0%0%0%
1. -2sin2xcos7x
2. -2sin7xcos2x
3. 2sin7xcos2x
4. 2sin2xcos7x
Use the figure to find the exact value of the trigonometric function
tan2
8
6
10
3
10
1
3
1. *
2. *
3. *
4. * 3
Find the exact value of the following using the half-angle formulas
cos2
* * * *
0% 0%0%0%
10
102
5
10
10
2
5
cos ,
4
5
3
2
1. *
2. *
3. *
4. *
Use the power-reducing formulas to find the exact value of the trigonometric function
1. *
2. *
3. *
4. *
cos27
12
* * * *
0% 0%0%0%
2 3
4
2 3
4
3 2
2
3 2
2
Use the power-reducing formulas to find the exact value of the trigonometric function
sin2 135o
* * * *
0% 0%0%0%
1
2
1
2
1 2
2
1 2
2
1. *
2. *
3. *
4. *
Find the exact value of sin2x using the double angle formulasin ,x x
1
15
3
2
* * * *
0% 0%0%0%
223
225
223
225
8 14
225
8 14
225
1. *
2. *
3. *
4. *
Find the exact values of sin2x and cos2x using the double angle formulasin ,x
8
15
3
22
* * * *
0% 0%0%0%
16 161
225
97
225,
97
225
16 161
225,
97
225
16 161
225,
16 161
225
97
225,
1. *
2. *
3. *
4. *