Exam 3 Flashcards by Lily Williams

Q

radio 0 degrees

A

0

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Q

radian 30 degrees

A

pi/6

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Q

radian 45 degrees

A

pi/4

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Q

radian 60 degrees

A

pi/3

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Q

radian 90 degrees

A

pi/2

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Q

sin0

A

0

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Q

sin 30

A

1/2

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Q

sin 45

A

sqrt2/2

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Q

sin 60

A

sqrt3/2

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Q

sin 90

A

1

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Q

cos 0

A

1

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Q

cos 30

A

sqrt 3/2

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Q

cos 45

A

sqrt 2/2

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Q

cos 60

A

1/2

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Q

cos 90

A

0

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Q

tan 0

A

0

Q

tan 30

A

sqrt3/3

Q

tan 45

A

1

Q

tan 60

A

sqrt 3

Q

tan 90

A

undef.

Q

3 Pythagorean Identities

A

sin²θ + cos²θ = 1
1 + cot2⁡x = csc2x
tan2x + 1 = sec2x

Q

secx =

A

1/cosx

Q

cscx =

A

1/sinx

Q

tanx =

A

sinx/cosx

Q

cotx =

A

cosx/sinx, 1/tanx

Q

Addition/Subtraction formulas: SINE

A

sin(a+b)= sinacosb + cosasinb
sin(a-b)= sinacosb-cosasinb

Q

Addition/Subtraction formulas: COSINE

A

cos(a+b)= cosacosb - sinasinb
cos(a-b)= cosacosb + sinasinb

Q

Addition/Subtraction formulas: TANGENT

A

tan(a+b)= (tana+tanb)/(1-tanatanb)
tan(a-b)= (tana-tanb)/(1+tanatanb)

Q

double identity: SINE

A

sin(2x)= 2sincosx

Q

double identity: COSINE

A

cos(2x)= cos2x-sin2x

Q

double identity: TANGENT

A

tan(2x)= (2tanx)/1-tan2x, aka, (tanx+tanx)/1-tanxtanx

Q

Half Angle: SINE

A

sin(u/2)= pos/neg square root of (1-cosu)/2

Q

Half Angle: COSINE

A

cos(u/2)= pos/neg sqrt (1+cosu)/2

Q

Half Angle: TANGENT

A

(1-cosu)/sinu, sinu/(1+cosu)

Q

Power Reduction: COSINE

A

cos2x= 1/2(1+cos(2x))

Q

Power Reduction: SINE

A

sin2x = 1/2 (1-cos(2x))

Q

Power Reduction: TANGENT

A

tan2x = (1-cos2x)/(1+cos2x)