AP Precalculus - Trig Identities

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32 Terms

1
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Reciprocal identity of sinx

sinx = 1/cscx

<p>sinx = 1/cscx</p>
2
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Reciprocal identity of cosx

cosx = 1/secx

<p>cosx = 1/secx</p>
3
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Reciprocal identity of tanx

tanx = 1/cotx

<p>tanx = 1/cotx</p>
4
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Reciprocal identity of cscx

cscx = 1/sinx

<p>cscx = 1/sinx</p>
5
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Reciprocal identity of secx

secx = 1/cosx

<p>secx = 1/cosx</p>
6
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Reciprocal identity of cotx

cotx = 1/tanx

<p>cotx = 1/tanx</p>
7
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Quotient identity of tanx

tanx = sinx/cosx

<p>tanx = sinx/cosx</p>
8
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Quotient identity of cotx

cotx = cosx/sinx

<p>cotx = cosx/sinx</p>
9
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Pythagorean identity of sin and cos

sin²x + cos²x = 1

cos²x = 1 - sin²x

sin²x = 1 - cos²x

cos²x + 1 = -sin²x

sin²x + 1 = -cos²x

<p>sin²x + cos²x = 1</p><p>cos²x = 1 - sin²x</p><p>sin²x = 1 - cos²x</p><p>cos²x + 1 = -sin²x</p><p>sin²x + 1 = -cos²x</p>
10
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Pythagorean identity of tan and sec

1 + tan²x = sec²x

tan²x = sec²x - 1

1 = sec²x - tan²x

<p>1 + tan²x = sec²x</p><p>tan²x = sec²x - 1</p><p>1 = sec²x - tan²x</p>
11
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Pythagorean identity of cot and csc

1 + cot²x = csc²x

cot²x = csc²x - 1

1 = csc²x - cot²x

<p>1 + cot²x = csc²x</p><p>cot²x = csc²x - 1</p><p>1 = csc²x - cot²x</p>
12
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Cofunction identity of sin

sin(Ď€/2 - x) = cosx

13
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Cofunction identity of cos

cos(Ď€/2 - x) = sinx

14
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Cofunction identity of tan

tan(Ď€/2 - x) = cotx

15
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Cofunction identity of cot

cot(Ď€/2 - x) = tanx

16
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Cofunction identity of sec

sec(Ď€/2 - x) = cscx

17
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Cofunction identity of csc

csc(Ď€/2 - x) = secx

18
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Odd identity of sin

sin(-x) = -sinx

19
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Odd identity of csc

csc(-x) = -cscx

20
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Even identity of cos

cos(-x) = cosx

21
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Even identity of sec

sec(-x) = secx

22
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Odd identity of tan

tan(-x) = -tanx

23
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Odd identity of cot

cot(-x) = -cotx

24
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Sum formula for sine

sin(u + v) = sin(u)cos(v) + cos(u)sin(v)

25
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Difference formula for sine

sin(u - v) = sin(u)cos(v) - cos(u)sin(v)

26
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Sum formula for cosine

cos(u + v) = cos(u)cos(v) - sin(u)sin(v)

27
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Difference formula for cosine

cos(u - v) = cos(u)cos(v) + sin(u)sin(v)

28
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Sum formula for tangent

tan(u + v) = (tan(u) + tan(v)) / (1 - tan(u)tan(v))

<p>tan(u + v) = (tan(u) + tan(v)) / (1 - tan(u)tan(v))</p>
29
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Difference formula for tangent

tan(u - v) = (tan(u) - tan(v)) / (1 + tan(u)tan(v))

<p>tan(u - v) = (tan(u) - tan(v)) / (1 + tan(u)tan(v))</p>
30
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Double angle formula for sine

sin(2x) = 2sin(x)cos(x)

<p>sin(2x) = 2sin(x)cos(x)</p>
31
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Double angle formula for cosine

cos(2x) = cos²x - sin²x

= 2cos²x - 1

= 1 - 2sin²x

<p>cos(2x) = cos²x - sin²x</p><p>= 2cos²x - 1</p><p>= 1 - 2sin²x</p>
32
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Double angle formula for tangent

tan(2x) = 2tan(x) / (1 - tan²x)

<p>tan(2x) = 2tan(x) / (1 - tan²x)</p>