Precalc.- Sums/Difference and Double Angles Practice
Name:
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In Problems i-20, find the exact value of each expression.
5. cos-{-
~) .
9. tan[ sin-{-
( Jv3)
v;)]
1L sec tan- 1
14. cos( sin-
( . 27T)
1
12. esc( sin-1
7
20. cos-{ cos ; )
18. cos-{ tan : )
1 .
.
If sin 8 = -3, 8 in quadrant II, find the exact value of:
(a) cos 8
Find the exact value. Show all work clearly. Box your fmal answer.
23.
tan15Y -tan20°
1+ tan15Y tan20°
25. cos[sin-• (-!)- tan-• (
27.
29 .. If
1
2
a) sin2B
. (2
Sill
7r
cosB =-,with--~ B ~ 0
2
~)
~)
3
17. sin-1 cos3
21.
4. sm. -!( - -21)
3. tan-1 1
2. cos-1 0
1. sin-1 1
COS -1
5)
U
1
1r
4
2
and sin/}=-, withO ~ fJ ~-
b) tan( e- /3)
~ )]
then find:
c) cos2/}
Identities II - Verify each identity. Show all steps clearly.
1.
'">
.)
.
sec8
1 +sec8
I
•
1-Sill
2
=
1-cos8
sin 8 COS 8
8 =--'---tan8
2. sin(a+P) =tana+tanp
cosacosp
4.
_
l-4sin 2 8+4sin 4 8 _
2
1
4
4
- 2 cos 8
cos 8-sin 8
Precalc.- Sums/Difference and Double Angles Practice
In Problems j -20, find the exact value of each expression.
1. sin-1 1
-rl/;r
s. cos-1( - ~)
9. tan[sin-
1
(-
2.
CJfl((p
.
cos-
1
0
1\j)-
-"'?)
6. tan-1 (-VJ)
~) J -D
10.
tan[ cos-{-~)] ~ 0
')
J ,.
17. sin-1
1\jJ
21.
-~ (a)
. 2r.)
(cos3
If sin 8 = .!_
3'
cosB
~
-
IS.
tan[sin-{ -i)J
-$
19.
tan-r( tan
1r(L/
7
;) -
Bin quadrant II, find the exact value of:
;> ,r;;_
(b)
sin(o + ~)
::
3
Find the exact value. Show all work clearly. Box your final answer.
23.
tan 155° -tan 20°
1 +tan155" tan20°
+0-Y\ (
0( -
~\'
-h..y')( ~ S5~ bJo)
+z._n ( , 3s)
27. sin(2cos-
1
2.)
12
~11
, 1I 7
s·,n((}· ~)
,,
5
b)
tan ( B- p) -= +c If',
e -
-tz,_.v,
f;
c) cos2P ::
Identities II - Verify each identity. Show all steps clearly.
1.•
sece
1-cose
=-1+ sec e
sin 2 e
-L
~~-
~+ ..L.
(oSt:r
CoStJ
::::
2. sin(a + P) =tan a+ tan,B
cosacosfJ
I!
\,
\
!
I
I
b
If
\.._..,)
I
l
I1
l
j
I
l
'l
Hl
-----'44'-
I
-.: : : S ~ V!-t:T (OS -€J
-----~-~-~-
----
-o,Jf 1-.p
<L
if\A~; f\
j
(r;;s{j
\
''\;
ll
\V
-:: cos-:.e
(J
\ j It
'"'--.)