Math& 142 – Using Trig Identities (section 7.1)
Winter 2016
Name:
Trig Identities we know so far….
Reciprocal Identities
csc x =
1
sin x
sec x =
1
cos x
tan x =
sin x
cos x
cot x =
cos x
sin x
cot x =
1
tan x
Pythagorean Identities
Even-Odd Identities
sin 2 x + cos2 x = 1
sin(−x) = −sin x
csc(−x) = −csc x
tan 2 x +1 = sec 2 x
cos(−x) = cos x
sec(−x) = sec x
1+ cot 2 x = csc 2 x
tan(−x) = − tan x
cot(−x) = −cot x
Cofunction Identities
sin( π2 − x) = cos x
tan( π2 − x) = cot x
sec( π2 − x) = csc x
cos( π2 − x) = sin x
cot( π2 − x) = tan x
csc( π2 − x) = sec x
Use trig identities to simplify each expression (rewrite each expression in a simpler way):
1.
cos x + tan x sin x
2.
sin x
cos x
+
cos x 1+ sin x
3.
tan x
sec x sin x
4.
1−
sin 2 x
1+ cos x
Math& 142 – Using Trig Identities (section 7.1)
Winter 2016
Name:
Use trig identities to prove each identity (start with one side of the identity and manipulate it - using known
identities - until it looks like the other side):
1.
sin 3 x + sin x cos2 x = sin x
2.
tan x
= sec x − cos x
csc x
3.
1− cos x
sin x
−
=0
sin x
1+ cos x
4.
csc x
= cos x
tan x + cot x
5.
cos x
= sec x + tan x
1− sin x
6.
1+ cos x
tan 2 x
=
cos x
sec x −1