Trig functions Calc

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26 Terms

1
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Sin²x+Cos²x

=1

2
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1 + tan²x

=sec²x

3
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cot²x+1

=csc²x

4
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sin2x

=2sinxcosx

5
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Sinx + cosx

=1/2 sin(2x)

6
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cos2x

=cos²x-sin²x

7
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sin²x

=(1-cos2x)/2

8
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cos²x

=(1+cos2x)/2

9
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√(a²-x²)

x = asinΘ
cos²Θ=1-sin²Θ

10
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√(a²+x²)

x=atanΘ
sec²Θ=1+tan²Θ

11
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√(x²-a²)

x=asecΘ
tan²Θ=sec²Θ-1

12
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∫sinudu

= -cosu + C

13
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∫cosudu

= sin u + C

14
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∫tanudu

= -ln|cosu| + C

15
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∫cscudu

= -ln|cscu + cotu| + C

16
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∫secudu

= ln|secu + tanu| + C

17
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∫cotudu

= ln|sinu| + C

18
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∫e^u du

= e^u + C

19
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∫1/u du

= ln|u| + C

20
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∫a^u du

= (a^u)/lna + C

21
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∫1/(1+x²)dx

= arctanx + C

22
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∫1/√(1-x²)dx

= arcsinx + C

23
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∫-1/√(1-x²)dx

= arccosx + C

24
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∫1/(a²+u²)du

= 1/a(arctan(u/a)) + C

25
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∫1/√(a²-u²)du

= arcsin(u/a) + C

26
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∫1/(u√(u²-a²))

= 1/a(arcsec(|u|/a) + C