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pre-calc 12 FormulaSheet

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C12 - 0.0 - Formula Sheet
𝑦 = π‘Žπ‘“ 𝑏(π‘₯ − β„Ž) + π‘˜
Polynomials
𝑦 = π‘Ž(π‘₯ − 𝑧) (π‘₯ − π‘Ÿ) (π‘₯ − 𝑠) …
π‘ π‘–π‘›πœƒ = 𝑦
πœ‹ = 180
π‘π‘œπ‘ πœƒ = π‘₯
𝐻
π‘π‘ π‘πœƒ = ⎯⎯
𝑂
𝐴
π‘π‘œπ‘‘πœƒ = ⎯⎯
𝑂
𝐻
π‘ π‘’π‘πœƒ = ⎯⎯
𝐴
Pythagorean Identities
πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ = (π‘₯ − π‘Ž)
𝑅=0
π‘₯ +𝑦 =1
𝑦
π‘‘π‘Žπ‘›πœƒ = ⎯⎯
π‘₯
(π‘π‘œπ‘ π‘₯, 𝑠𝑖𝑛π‘₯)
2∗ πœ‹
𝑝 = ⎯⎯⎯
|𝑏|
𝑂
πœƒ ∗ = sin (+ ⎯⎯)
𝐻
sin πœƒ + cos πœƒ = 1
π‘₯≥𝑐
π‘Ž π‘†π‘¦π‘›π‘‘β„Žπ‘’π‘‘π‘–π‘ = 𝑓(π‘Ž) = π‘₯ − 𝑖𝑛𝑑 (π‘Ž, 0)
𝑃(π‘₯)
𝑅
⎯⎯⎯⎯⎯= 𝑄(π‘₯) + ⎯⎯⎯⎯⎯
π‘₯−π‘Ž
π‘₯−π‘Ž
Trigonometry
⎯⎯⎯⎯⎯
√π‘₯ − 𝑐
Radicals
Transformations
πœƒ
± 𝑝∗ 𝑛, 𝑛 ∈ 𝐼
=πœƒ
1 + tan πœƒ = sec πœƒ
1 + cot πœƒ = csc πœƒ
Reciprocal and Quotient Identities
1
π‘ π‘’π‘πœƒ = ⎯⎯⎯⎯
π‘π‘œπ‘ πœƒ
1
π‘π‘ π‘πœƒ = ⎯⎯⎯⎯
π‘ π‘–π‘›πœƒ
1
π‘π‘œπ‘‘πœƒ = ⎯⎯⎯⎯⎯
π‘‘π‘Žπ‘›πœƒ
π‘ π‘–π‘›πœƒ
π‘‘π‘Žπ‘›πœƒ = ⎯⎯⎯⎯
π‘π‘œπ‘ πœƒ
π‘π‘œπ‘ πœƒ
π‘π‘œπ‘‘πœƒ = ⎯⎯⎯⎯
π‘ π‘–π‘›πœƒ
Addition Identities
sin(𝛼 + 𝛽) = 𝑠𝑖𝑛𝛼 π‘π‘œπ‘ π›½ + π‘π‘œπ‘ π›Ό 𝑠𝑖𝑛𝛽
cos(𝛼 + 𝛽) = π‘π‘œπ‘ π›Ό π‘π‘œπ‘ π›½ − 𝑠𝑖𝑛𝛼 𝑠𝑖𝑛𝛽
sin(𝛼 − 𝛽) = 𝑠𝑖𝑛𝛼 π‘π‘œπ‘ π›½ − π‘π‘œπ‘ π›Όπ‘ π‘–π‘›π›½
cos(𝛼 − 𝛽) = cos 𝛼 π‘π‘œπ‘ π›½ + 𝑠𝑖𝑛𝛼 𝑠𝑖𝑛𝛽
Double Angle Identities
Arc Length/Sector Area
π‘Žπ‘Ÿ
πœƒπ‘Ÿ
π‘Ž = πœƒπ‘Ÿ
𝐴 = ⎯⎯⎯ 𝐴 = ⎯⎯⎯
2
2
π‘π‘œπ‘ 2πœƒ = cos πœƒ − sin πœƒ
= 2 cos πœƒ − 1
= 1 − 2 sin πœƒ
𝑠𝑖𝑛2πœƒ = 2π‘ π‘–π‘›πœƒπ‘π‘œπ‘ πœƒ
π‘‘π‘Žπ‘›π›Ό + π‘‘π‘Žπ‘›π›½
tan(𝛼 + 𝛽) = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
1 − π‘‘π‘Žπ‘›π›Ό π‘‘π‘Žπ‘›π›½
Exponentials
log π‘Ž = 𝑐
π‘Ž > 0, 𝑏 > 0, 𝑏 ≠ 1
Rationals
𝑉𝐴 ≠ 0
π‘™π‘œπ‘” π‘Ž
π‘Ž=𝑏
π‘Ž
𝑦 = ⎯⎯⎯+ 𝐻𝐴
𝑉𝐴
Combinatorics
π‘Ÿ
𝐹 = 𝑃 1 ± ⎯⎯
𝑛
𝐹 = 𝑃(1 ± π‘Ÿ)
Logarithms
2 tan πœƒ
tan 2πœƒ = ⎯⎯⎯⎯⎯⎯⎯⎯⎯
1 − tan πœƒ
π‘‘π‘Žπ‘›π›Ό − π‘‘π‘Žπ‘›π›½
tan(𝛼 − 𝛽) = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
1 + π‘‘π‘Žπ‘›π›Ό π‘‘π‘Žπ‘›π›½
π‘Žπ‘₯
𝑦 = ⎯⎯⎯⎯
𝑏π‘₯
𝑛!
𝑃 = ⎯⎯⎯⎯⎯⎯⎯
(𝑛 − π‘Ÿ)!
= π‘šπ‘™π‘œπ‘”π‘Ž
𝐹 = 𝑃(π‘Ÿ)⎯⎯
𝐹 = 𝑃𝑒
π‘™π‘œπ‘”π‘Ž
log π‘Ž = ⎯⎯⎯⎯⎯
π‘™π‘œπ‘” 𝑏
π‘Ž(𝐻𝐴) (π‘₯ − 𝑖𝑛𝑑)(β„Žπ‘œπ‘™π‘’π‘ )
𝑦 = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
(𝐻𝐴)(𝑉𝐴 𝑠)(β„Žπ‘œπ‘™π‘’π‘ )
𝑛!
𝐢 = ⎯⎯⎯⎯⎯⎯⎯⎯⎯
(𝑛
π‘Ÿ! − π‘Ÿ)!
𝐼 = 10
π‘™π‘œπ‘” π‘š + π‘™π‘œπ‘” 𝑛 = π‘™π‘œπ‘” π‘šπ‘›
π‘š
π‘™π‘œπ‘” π‘š − π‘™π‘œπ‘” 𝑛 = π‘™π‘œπ‘” ⎯⎯
𝑛
𝑅
𝑦 = π΄π‘ π‘¦π‘šπ‘π‘‘π‘œπ‘‘π‘’ + ⎯⎯⎯⎯⎯⎯⎯
π·π‘–π‘£π‘–π‘ π‘œπ‘Ÿ
(π‘Ž + 𝑏)
𝑑
knackacademics.com PreCalc12PC - 604.505.2867 Page 1
=
𝐢 π‘Ž
𝑏
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