Calculus 2 - Trig Identities

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dy/dx sin x

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32 Terms

1

dy/dx sin x

= cos x

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2

dy/dx cos x

= -sin x

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3

dy/dx tan x

= sec^2(x)

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4

dy/dx cot x

= -csc^2(x)

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5

dy/dx sec x

= sec x tan x

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6

dy/dx csc x

= csc x cot x

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7

∫ sin x dx

= -cos x + C

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8

∫ cos x dx

= sin x + C

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9

∫ tan x dx

= ln |sec x| + C

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10

∫ cot x dx

= ln |sin x| + C

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11

∫ sec x dx

= ln |sec x + tan x| + C

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12

∫ csc x dx

= ln |csc x + cot x| + C

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13

∫ 1/x dx

= ln |x| + C

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14

cos(2x)

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

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15

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

= 1

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16

sin (2x)

= 2 sin x cos x

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17

cos^2(x)

= 1 - sin^2(x)

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18

cos^2(x)

= (1+cos2x) / 2

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19

sin^2(x)

= 1 - cos^2(x)

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20

sin^2(x)

= 1 - cos (2x) / 2

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21

∫ e^kx dx

= e^kx / k + C

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22

∫ sec^2(x)

= tan x + C

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23

∫ csc^2(x) dx

= -cot x + C

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24

∫ csc x cot x dx

= -csc x + C

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25

1 + cot^2(x)

= csc^2(x)

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26

tan^2(x) + 1

= sec^2(x)

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27

What trig substitution does √(a^2 - x^2) belong with ? What is it's identity?

x = a sin θ; 1 - sin^2(x) = cos^2(x)

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28

What trig substitution does √(a^2 + x^2) belong with ? What is it's identity?

x = a tan θ; 1 + tan^2(x) = sec^2(x)

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29

What trig substitution does √(x^2 - a^2) belong with ? What is it's identity?

x = a sec θ; sec^2(x) - 1 = tan^2(x)

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30

How do you tell if a function is convergent?

The answer to the integral is a finite number.

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31

How can you tell if a function is divergent?

The answer to the integral is an infinite number (infinity).

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32

What is the integration by parts formula?

∫u dv = uv - ∫v du

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