unit 5 formulas Flashcards

1
Q

sin^2x + cos^2x = ?

A

1

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2
Q

sin^2x = ?

A

1 - cos^2x

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3
Q

cos^2x = ?

A

1 - sin^2x

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4
Q

sec^2x - tan^2x = ?

A

1

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5
Q

sec^2x = ?

A

1 + tan^2x

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6
Q

tan^2x = ?

A

sec^2x - 1

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7
Q

csc^2x - cot^2x = ?

A

1

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8
Q

csc^2x = ?

A

1 + cot^2x

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9
Q

cot^2x = ?

A

csc^2x - 1

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10
Q

sin (a + b)

A

sin a cos b + cos a sin b

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11
Q

sin (a - b)

A

sin a cos b - cos a sin b

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12
Q

cos (a + b)

A

cos a cos b - sin a sin b

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13
Q

cos (a - b)

A

cos a cos b + sin a sin b

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14
Q

tan (a + b)

A

(tan a + tan b) / 1 - tan a tan b

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15
Q

tan (a - b)

A

(tan a - tan b) / 1 + tan a tan b

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16
Q

sin 2x

A

2 sin x cos x

17
Q

cos 2x (variation 1)

A

cos^2x - sin^2x

18
Q

cos 2x (variation 2)

A

2cos^2x - 1

19
Q

cos 2x (variation 3)

A

1 - 2sin^2x

20
Q

tan 2x

A

(2 tan x) / 1 - tan^2x

21
Q

sin^2x

A

(1 - cos 2x) / 2

22
Q

cos^2x

A

(1 + cos 2x) / 2

23
Q

tan^2x

A

(1 - cos 2x) / (1 + cos 2x)

24
Q

for half angle identities, how do you decide if the square root is positive or negative

A

see what quadrant x/2 is in, and see if the sin/cos/tan whatever of x/2 is positive or negative

25
Q

sin(x/2)

A

+/- sqrt((1 - cos x) / 2)

26
Q

cos(x/2)

A

+/- sqrt((1 + cos x) / 2)

27
Q

tan(x/2)

A

+/- sqrt((1- cos x) / (1 + cos x))