Calc Exam !

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Last updated 12:42 AM on 10/1/26
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16 Terms

1
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Pythagorean (sin and cos)

sin²+cos²=1 → sin²=1-cos²→ cos²=1-sin²

2
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Pythagorean (tan and sec)

Sec²= Tan²+1 → Tan²= sec²-1

3
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Double-Angle Formulas

sin(2x)=2sin(x)cos(x) → cos(2x)= cos²(x)-sin²(x)

4
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Half-angle formulas

sin²(x)=1/2[1-cos(2×)] → cos²=1/2[1+cos(2x)]

5
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Integration by parts

uv-Svdu

6
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Ssec(x)tan(x)

sec(x)

7
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d/dx sec(x)

sec(x)tan(x)

8
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Ssec²(x)

tan(x)

9
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d/dx tan(x)

sec²(x)

10
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Stan(x)

ln|sec²(x)+1|+c

11
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Ssec(x)

ln|sec(x)+tan(x)|

12
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Ssec³(x)

1/2[sec(x)tan(x)+ln|sec(x)+tan(x)|]+c

13
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sqrt(x²-a²)

x=asec(θ)

14
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sqrt(a²-x²)

x=asin(θ)

15
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sqrt(a²+x²)

x=atan(θ)

16
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1/x²+a²

=(1/a) arctan(x/a)