TRIGONOMETRIC IDENTITIES

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35 Terms

1

Pythagorean Identity sin cos

sin²x + cos²x = 1

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2

Pythagorean Identity tan sec

1 + tan²x = sec²x

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3

Pythagorean Identity cot csc

1 + cot²x = csc²x

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4

Reciprocal Identity of sin

sin x = 1/csc x

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5

Reciprocal Identity of cos

cos x = 1/sec x

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6

Reciprocal Identity of tan

tan x = 1/cot x

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7

Reciprocal Identity of csc

csc x = 1/sin x

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8

Reciprocal Identity of sec

sec x = 1/cos x

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9

Reciprocal Identity of cot

cot x = 1/tan x

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10

Even-Odd Identity sin

sin(-x) = -sin x

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11

Even-Odd Identity cos

cos(-x) = cos x

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12

Even-Odd Identity tan

tan(-x) = -tan x

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13

Even-Odd Identity sec

sec(-x) = sec x

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14

Even-Odd Identity cot

cot(-x) = -cot x

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15

Even-Odd Identity csc

csc(-x) = -csc x

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16

Double-Angle Identity for sin

sin 2x = 2sin x cos x

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17

Double-Angle Identity for cos

cos 2x = 1 - 2sin²x

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18

Double-Angle Identity for tan

tan 2x = 2tan x / (1 - tan²x)

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19

Derivative of sin

d/dx sin x = cos x

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20

Derivative of cos

d/dx cos x = -sin x

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21

Derivative of tan

d/dx tan x = sec²x

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22

Derivative of cot

d/dx cot x = -csc²x

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23

Derivative of sec

d/dx sec x = sec x tan x

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24

Derivative of csc

d/dx csc x = -csc x cot x

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25

Integral of sin

∫ sin x dx = -cos x + C

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26

Integral of cos

∫ cos x dx = sin x + C

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27

Integral of tan

∫ tan x dx = ln(sec x) + C

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28

Integral of cot

∫ cot x dx = ln(sin x) + C

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29

Integral of sec

∫ sec x dx = ln(sec x + tan x) + C

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30

Integral of csc

∫ csc x dx = ln(csc x - cot x) + C

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31

Power Reducing Identity for sin

sin²x = (1 - cos 2x)/2

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32

Power Reducing Identity for cos

cos²x = (1 + cos 2x)/2

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33

Power Reducing Identity for tan

tan²x = (1 - cos 2x)/(1 + cos 2x)

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34

Tangent Identity

tan x = sin x / cos x

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35

Cotangent Identity

cot x = cos x / sin x

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