Trigonometric Identities Flashcards by Erin boeger

Q

sin ø

A

Opposite/ Hypotenuse

the “y” coordinate

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Q

cos ø

A

Adjacant / Hypotenuse

the “x” coordinate

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Q

tan ø

A

Opposite / Adjacant

sin ø / cos ø

y / x

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Q

csc ø

A

Hypotenuse / Opposite

1 / sin ø

1 / y

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Q

sec ø

A

Hypotenuse / Adjacent

1 / cos ø

1 / x

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Q

cot ø

A

Adjacent / Opposite

cosø / sinø
x / y

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Q

sin²ø + cos²ø =

A

1

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Q

tan²ø +1 =

A

sec²ø

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Q

cot²ø + 1 =

A

csc²ø

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Q

sin(2ø)

A

2sin(ø)cos(ø)

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Q

cos(2ø)

A

cos²ø - sin²ø

2cos²ø - 1

1 - 2sin²ø

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Q

tan(2ø)

A

2tan ø / 1 - tan²ø

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Q

Law of Sines

A

sina / A = sinb / B = sinc / C

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Q

Law of Cosines

A

a² = b² + c² - 2bc cos(a)

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Q

Derivative of sin ø

A

f(ø) = sin ø

f^’(ø) = cos ø

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Q

Derivative of cos ø

A

f(ø) = cos ø

f^’(ø) = -sin ø

Q

Derivative of tan ø

A

f(ø) = tan ø

f^’(ø) = sec²(ø)

Q

Derivative of cot ø

A

f(ø) = cot ø

f^’(ø) = -csc²(ø)

Q

Derivative of sec ø

A

f(ø) = sec ø

f^’(ø) = sec(ø)tan(ø)

Q

Derivative of csc ø

A

f(ø) = csc ø

f^’(ø) = -csc(ø)cot(ø)

Q

What’s the domain of sin ø

A

domain of sin ø can be any angle

Q

What is the period of sin ø

A

The period of sin(wø) -> T = 2π / w

Q

What is the range of sin ø

A

-1 < sin ø < 1

Q

What is the domain of cos ø

A

cos ø can be any angle

Q

What is the period of cos ø

A

cos(wø) -> T = 2π / w

Q

What is the range of cos ø

A

-1 < cos ø < 1

Q

What is the domain of tan ø

A

tan ø, ø != (n + 1/2)π, n = 0,^<u>+</u>1,^<u>+</u>2..

Q

What is the range of tan ø

A

-(inf) < tan ø < (inf)

Q

What is the period of tan ø

A

tan(wø) -> T = π / w

Q

What is the domain of csc ø

A

domain of csc ø, ø != nπ, n = 0,^<u>+</u>1,^<u>+</u>2,…

Q

What is the range of csc ø

A

csc ø > 1 and csc ø < -1

Q

What is the period of csc ø

A

period csc(wø) -> T= 2π / w

Q

What is the domain of sec ø

A

domain of sec ø, ø != (n+1/2)π, n = 0,^<u>+</u>1,^<u>+</u>2,…

Q

What is the range of sec ø

A

sec ø > 1 and sec ø < -1

Q

What is the period of sec ø

A

period of sec(wø) -> T = 2π / w

Q

What is the domain of cot

A

domain of cot ø, ø != nπ, n = ^<u>+</u>1,^<u>+</u>2,…

Q

What is the range of cot ø

A

-(inf) < cot ø < (inf)

Q

What is the period of cot ø

A

period of cot(wø) -> T = π / w