Trigonometry Cheat Sheet

This is the list of frequently used formulas in Trigonometry calculations


Basic Formulas:
sin Θ = opposite / hypotenuse
cos Θ = adjacent / hypotenuse
tan Θ = opposite / adjacent
csc Θ = hypotenuse / opposite
sec Θ = hypotenuse / adjacent
cot Θ = adjacent /opposite

Range of All possible value for Sin, cos, tan, csc, sec and cot
-1≤ sinΘ ≤ 1
-1≤ cosΘ ≤ 1
-∞ < tanΘ < ∞
cscΘ ≥ 1 and ≤ -1
secΘ ≥ 1 and ≤ -1
-∞ < cotΘ < ∞

Unit Circle for Trigonometry Cheat Sheet



In any ABC triangle,

Sine formula:
a / sin A = b / sin B = c / sin C = 2R
where R is the radius of the triangle.

Cosine formula:
a2 = b2 + c2 - 2bc cos A

Napier's formula:
tan (A - B) / 2 = [(a - b) / (a + b)] cot (c / 2)

Projection Formula:
a = b cos C + c cos B

sub-multiple angle:
1. sin (A/2) = √[(s - b)(s - a) / bc]
2. cos (A/2) = √[s (s - a) / bc]
3. tan (A/2) = √[(s - b)(s - c) / s (s - a)]
where s = (a + b + c) / 2
Tangent formula:
(a + b)/(a - b) = tan ((A + B) / 2) / tan ((A - B) / 2)

Area formula: (∆ - Area)
1. ∆ = ab sin C / 2
2. ∆ = abc / 4R
3. ∆ = √[s (s - a)(s - b)(s - c)]
4. ∆ = (s - a)(s - b)(s - c) / r