Trigonometric Identities

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Memorize the trigonometric identities!

Math

AP Calculus AB

10th

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35 Terms

1
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csc(x)

=1/sin(x)

2
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sec(x)

=1/cos(x)

3
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cot(x)

=1/tan(x)

4
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tan(x)

=sin(x)/cos(x)

5
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cot(x)

=cos(x)/sin(x)

6
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sin^2(x)+cos^2(x)

=1

7
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tan²(x)+1

=sec²(x)

8
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1+cot^2(x)

=csc^2(x)

9
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sin(-x)

=-sin(x)

10
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cos(-x)

=cos(x)

11
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tan(-x)

=-tan(x)

12
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csc(-x)

=-csc(x)

13
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sec(-x)

=sec(x)

14
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cot(-x)

=-cot(x)

15
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sin((pi/2)-u)

=cos(u)

16
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cos((pi/2)-u)

=sin(u)

17
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tan((pi/2)-u)

=cot(u)

18
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sin(x+y)

=sin(x)cos(y)+cos(x)sin(y)

19
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sin(x-y)

=sin(x)cos(y)-cos(x)sin(y)

20
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cos(x+y)

=cos(x)cos(y)-sin(x)sin(y)

21
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cos(x-y)

=cos(x)cos(y)+sin(x)sin(y)

22
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tan(x+y)

=(tan(x)+tan(y))/(1-tan(x)tan(y))

23
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tan(x-y)

=(tan(x)-tan(y))/(1+tan(x)tan(y))

24
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sin(2x)

=2sin(x)cos(x)

25
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cos(2x)

=cos^2(x)-sin^2(x), 1-sin^2(x), 2cos^2(x)-1

26
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tan(2x)

=(2tan(x))/(1-tan²(x))

27
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sin(u/2)

=sqrt((1-cos(u))/2)

28
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cos(u/2)

=sqrt((1+cos(u))/2)

29
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tan(u/2)

=(1-cos(u))/sin(u)

=sin(u)/1+cos(u)

30
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d/dx(sin(x))

=cos(x)

31
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d/dx(cos(x))

=-sin(x)

32
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d/dx(tan(x))

=sec²(x)

33
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d/dx(csc(x))

=-csc(x)cot(x)

34
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d/dx(sec(x))

=sec(x)tan(x)

35
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d/dx(cot(x))

=-csc²(x)