Transcript TRIG IDENTITIES

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Homework questions?
3 Identities to Memorize:
2
sin Ө
+
2
cos Ө
=1
1 + tan2Ө = sec2Ө
1+
2
cos Ө
=
2
csc Ө
***NOTE
tan2Ө means (tanӨ)2
Example
If tanӨ=20˚, then tan2Ө = (20˚)2
Example 1
If tanӨ = 4/9, find secӨ
Which identity would you use?
The one that mentions tan and sec!!
Example 1
If tanӨ = 4/9, find secӨ
1 + tan2Ө = sec2Ө
1 + (4/9)2 = sec2Ө
81 + 16 = sec2Ө
81 81
97 = sec2Ө
81
secӨ = √97
9
Example 2
If sinӨ = 6/10, find cosӨ
Which identity would you use?
The one that mentions sin and cos!!
Example 2
If sinӨ = 6/10, find cosӨ
sin2Ө + tan2Ө = 1
(6/10)2 + cos2Ө = 1
cos2Ө = 100 - 36
100 100
cos2Ө = 64
100
cosӨ = 8 or -8
10
10
Example 3
Reduce the following identity to a single term:
csc2Ө - cot2Ө - sin2Ө
= (1 + cot2Ө) - cot2Ө -sin2Ө
= 1 - sin2Ө
= cos2Ө
Example 4
Reduce the following to a single term:
cosx ∙ cscx
= cosx ∙ 1
sinx
= cosx
sinx
= cotx
HOMEWORK
Workbook
p.244-245
#3, 4, 8