Trig Identities

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Pre-Calculus

Trig

Trigonometry

University/Undergrad

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34 Terms

1
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Pythagorean Identity for Sine and Cosine

sin^2x + cos^2x = 1

<p>sin^2x + cos^2x = 1</p>
2
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Pythagorean Identity for Tangent and Secant

1 + tan^2x = sec^2x

<p>1 + tan^2x = sec^2x</p>
3
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Pythagorean Identity for Cotangent and Cosecant

1 + cot^2x = csc^2x

<p>1 + cot^2x = csc^2x</p>
4
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Quotient Identity of Tangent

sinx/cosx

<p>sinx/cosx</p>
5
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Quotient Identity of Cotangent

cosx/sinx

<p>cosx/sinx</p>
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Reciprocal Identity of Sine

1/cscx

<p>1/cscx</p>
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Reciprocal Identity of Cosecant

1/sinx

<p>1/sinx</p>
8
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Reciprocal Identity of Cosine

1/secx

<p>1/secx</p>
9
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Reciprocal Identity of Secant

1/cosx

<p>1/cosx</p>
10
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Reciprocal Identity of Tangent

1/cotx

<p>1/cotx</p>
11
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Reciprocal Identity of Cotangent

1/tanx

<p>1/tanx</p>
12
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Sum of Two Angles Sine

sin(A+B) = sinAsinB + cosAcosB

<p>sin(A+B) = sinAsinB + cosAcosB</p>
13
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Difference of Two Angles Sine

sin(A-B) = sinAsinB - cosAcosB

<p>sin(A-B) = sinAsinB - cosAcosB</p>
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Sum of Two Angles Cosine

cos(A+B) = cosAcosB - sinAsinB

<p>cos(A+B) = cosAcosB - sinAsinB</p>
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Difference of Two Angles Cosine

cos(A-B) = cosAcosB + sinAsinB

<p>cos(A-B) = cosAcosB + sinAsinB</p>
16
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Sum of Two Angles Tangent

tan(A+B) = [tanA + tanB] / [ 1 - tanAtanB]

<p>tan(A+B) = [tanA + tanB] / [ 1 - tanAtanB]</p>
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Difference of Two Angles Tangent

tan(A-B) = [tanA - tanB] / [ 1 + tanAtanB]

<p>tan(A-B) = [tanA - tanB] / [ 1 + tanAtanB]</p>
18
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Double Angle: sin2x

2sinxcosx

<p>2sinxcosx</p>
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Double Angle: tan2x

[2tanx] / [ 1- tan^2 x ]

<p>[2tanx] / [ 1- tan^2 x ]</p>
20
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Double Angle: cos2x

cos^2 x - sin^2 x

<p>cos^2 x - sin^2 x</p>
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(Derivation) Double Angle: cos2x

1- 2sin^2 x

<p>1- 2sin^2 x</p>
22
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Negative Angle Formula: sin (-x)

-sinx

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Negative Angle Formula: cos (-x)

cosx

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Negative Angle Formula: tan (-x)

-tanx

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Negative Angle Formula: csc (-x)

-cscx

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Negative Angle Formula: sec (-x)

secx

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Negative Angle Formula: cot (-x)

-cotx

28
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Power Reducing Identity: sin^2 x

sin^2 x = [1 - cos (2x)] / 2

<p>sin^2 x = [1 - cos (2x)] / 2</p>
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Power Reducing Identity: cos^2 x

cos^2 x = [1 + cos (2x)] / 2

<p>cos^2 x = [1 + cos (2x)] / 2</p>
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Power Reducing Identity: tan^2 x

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

<p>[ 1 - cos (2x)] / [ 1 + cos (2x)]</p>
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Half Angle Formula for Sine

+/- square root of [ ( 1 - cosx ) / 2 ]

<p>+/- square root of [ ( 1 - cosx ) / 2 ]</p>
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Half Angle Formula for Cosine

+/- square root of [ ( 1 + cosx ) / 2 ]

<p>+/- square root of [ ( 1 + cosx ) / 2 ]</p>
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Half Angle Formula for Tangent

+/- square root of [( 1-cosx) / (1 + cosx)]

<p>+/- square root of [( 1-cosx) / (1 + cosx)]</p>
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(Derivation) Half Angle Formula for Tangent

sinx / (1 + cos x)

<p>sinx / (1 + cos x)</p>