math 6.5 - trigonometric identities

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Description and Tags

odd/even function symmetry, translation, pythagorean, compound angle, double angle

23 Terms

1

sin(-θ)

-sin(θ)

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2

cos(-θ)

cos(θ)

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3

tan(-θ)

-tan(θ)

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4

csc(-θ)

-csc(θ)

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5

sec(-θ)

sec(θ)

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6

cot(-θ)

-cot(θ)

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7

sin(π/2 - θ)

cos(θ)

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8

cos(π/2 - θ)

sin(θ)

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9

tan(π/2 - θ)

cot(θ)

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10

csc(π/2 - θ)

sec(θ)

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11

sec(π/2 - θ)

csc(θ)

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12

cot(π/2 - θ)

tan(θ)

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13

sin²(θ) + cos²(θ)

1

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14

sec²(θ)

1 + tan²(θ)

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15

csc²(θ)

1 + cot²(θ)

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16

sin(α ± β)

sin(α)cos(β) ± cos(α)sin(β)

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17

cos(α ± β)

cos(α)cos(β) ∓ sin(α)sin(β)

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18

tan(α ± β)

(tan(α) ± tan(β)) / (1 ∓ tan(α)tan(β))

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19

sin(2θ)

2cos(θ)sin(θ)

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20

cos(2θ) (i)

cos²(θ) - sin²(θ)

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21

cos(2θ) (ii)

2cos²(θ) - 1

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22

cos(2θ) (iii)

1 - 2sin²(θ)

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23

tan(2θ)

(2tan(θ)) / (1 - tan²(θ))

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