10. Use a half angle formula to determine the exact value of tan

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter11: Introduction To Trigonometry
Section11.CT: Test
Problem 3CT
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Solve the following problem using the half angle identity.
10. Use a half angle formula to determine the exact value of tan
(4).
Transcribed Image Text:10. Use a half angle formula to determine the exact value of tan (4).
PERIODIC I
IDENTITIES
PYTHAGOREAN IDENTITIES
sin? 0 + cos? e = 1
sin (8 + 2
sin e =
csc e
tan? 0 + 1 = sec2 0
cos(0 +2
cos e =
sec e
1
tan e =
cot?e +1 = csc20
tan(e + Te
cot e
csc(e + 2
LE IDENTITIES
HALF ANGLE IDENTITIES
in e cos e
sec(0 + 2
()-
1-
=±
- cos 8
sin
=2e - sin? 0
cot(e + T
2
1+ cos e
LAW OF CC
cos
a? = b? +
b2 = a? +
an e
can? e
1 cos 0
tan
1+ cos 0
c2 = a? +
SUM TO PRODUCT IDENTITIES
LAW OF SIN
sin a + sin B = 2 sin
(a +B
COS
sin a
sim
a
sin a – sin B = 2 cos
a+B
sin
LAW OF TA
%3D
Cos a + cos B = 2 cos (a+ B)
(α-β)
a - b
tar
2.
+1
Transcribed Image Text:PERIODIC I IDENTITIES PYTHAGOREAN IDENTITIES sin? 0 + cos? e = 1 sin (8 + 2 sin e = csc e tan? 0 + 1 = sec2 0 cos(0 +2 cos e = sec e 1 tan e = cot?e +1 = csc20 tan(e + Te cot e csc(e + 2 LE IDENTITIES HALF ANGLE IDENTITIES in e cos e sec(0 + 2 ()- 1- =± - cos 8 sin =2e - sin? 0 cot(e + T 2 1+ cos e LAW OF CC cos a? = b? + b2 = a? + an e can? e 1 cos 0 tan 1+ cos 0 c2 = a? + SUM TO PRODUCT IDENTITIES LAW OF SIN sin a + sin B = 2 sin (a +B COS sin a sim a sin a – sin B = 2 cos a+B sin LAW OF TA %3D Cos a + cos B = 2 cos (a+ B) (α-β) a - b tar 2. +1
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