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Trigonometric Identities and Formulas Reference Sheet, Study notes of Trigonometry

Various trigonometric identities and formulas, including pythagorean identities, double angle identities, half angle identities, tangent formulas, addition and subtraction formulas, and product to sum formulas.

What you will learn

  • What are the Pythagorean identities in trigonometry?
  • How do you find the value of cos(2x) using the given identities?
  • What is the formula for sin(A+B) in terms of sin A and cos B?

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

johnatan
johnatan 🇺🇸

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Trigonometric Reference Sheet
Pythagorean Identities
sin2x + cos2x = 1 (1)
1 + cot2x = csc2x (2)
tan2x + 1 = sec2x (3)
Double Angle Identities
sin(2x) = 2*sin x*cos x (4)
cos(2x) = cos2x - sin2x (5)
cos(2x) = 2*cos2x 1 (6)
cos(2x) = 1 2*sin2x (7)
Half Angle identities
cos2x = 1
2 (1+cos(2x)) (8)
sin2x = 1
2 (1 cos(2x)) (9)
Tangent formulas
tan x = sin 𝑥
cos 𝑥 (10)
𝑑
𝑑𝑥 tan x = sec2x (11)
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Trigonometric Reference Sheet

Pythagorean Identities sin^2 x + cos^2 x = 1 (1) 1 + cot^2 x = csc^2 x (2) tan^2 x + 1 = sec^2 x (3) Double Angle Identities sin(2x) = 2sin xcos x (4) cos(2x) = cos^2 x - sin^2 x (5) cos(2x) = 2cos^2 x – 1 (6) cos(2x) = 1 – 2sin^2 x (7) Half Angle identities cos^2 x = 1 2 (1+cos(2x)) (8) sin^2 x = 1 2 (1 – cos(2x)) (9) Tangent formulas tan x = sin 𝑥 cos 𝑥

𝑑 𝑑𝑥 tan x = sec^2 x (11)

Addition and Subtraction formulas sin(A+B) = sin Acos B + cos Asin B (12) sin(A – B) = sin Acos B – cos Asin B (13) cos(A+B) = cos Acos B – sin Asin B (14) cos(A – B) = cos Acos B + sin Asin B (15) Product to Sum formulas sin A sin B = 1 2 cos(A – B) – 1 2 cos(A + B) (16) cos A cos B = 1 2 cos(A – B) + 1 2 cos(A + B) (17) sin A cos B = 1 2 sin(A + B) + 1 2 sin(A - B) (18) cos A sin B = 1 2 sin(A + B) – 1 2 sin(A - B) (19)