trig identities and equations
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Last updated 4:26 PM on 1/28/25
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33 Terms
1
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sin^2x+cos^2x
=1
2
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cos^2x-sin^2x
=cos2x
3
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1+cot^2x
=csc^2x
4
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tan^2x+1
=sec^2x
5
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sinx
=1/cscx
6
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cosx
=1/secx
7
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tanx
=1/cotx
8
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cos(-x)
=cosx
9
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sec(-x)
=secx
10
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tan(-x) or -tanx
=sin(-x)/cos(-x)
11
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even
cosx, secx
12
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odd
sinx, cscx, tanx, cotx
13
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sin(pi/2-x)
=cosx
14
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cos(pi/2-x)
=sinx
15
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tan(pi/2-x)
=cotx
16
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csc(pi/2-x)
=secx
17
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sec(pi/2-x)
=cscx
18
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cot(pi/2-x)
=tanx
19
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sin(u+v)
= sin(u)cos(v) + cos(u)sin(v)
20
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sin(u-v)
= sin(u)cos(v)-cos(u)sin(v)
21
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cos(u+v)
= cos(u)cos(v)-sin(u)sin(v)
22
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cos(u-v)
= cos(u)cos(v) + sin(u)sin(v)
23
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tan(u+v)
= tan(u)+tan(v)/1-tan(u)tan(v)
24
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tan(u-v)
= tan(u)-tan(v)/1+tan(u)tan(v)
25
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sin2(u)
= 2sin(u)cos(u)
26
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tan2(u)
= 2tan(u)/1-tan(u)^2
27
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cos2(u)
cos^2(u)-sin^2(u) OR 2cos^2(u)-1 OR 1-2sin^2(u)
28
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θ
full angle
29
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θ/2
half angle
30
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The + or - depends on the __ in which θ/2 lies
quadrant
31
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sin θ/2
± √ (1 - cosθ)/2
32
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cos θ/2
± √(1 + cos θ)/2
33
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tan θ/2
±√(1-cosθ)/(1+cosθ)
