Summary Complete trigonometry formula sheet - Quick revision

Trigonometry Formula Sheet - Quick Revision

1. Basic Trigonometric Ratios
sin theta = Opposite / Hypotenuse
cos theta = Adjacent / Hypotenuse
tan theta = Opposite / Adjacent = sin theta / cos theta
cot theta = 1 / tan theta = cos theta / sin theta
sec theta = 1 / cos theta
csc theta = 1 / sin theta

2. Pythagorean Identities
sin^2 theta + cos^2 theta = 1
1 + tan^2 theta = sec^2 theta
1 + cot^2 theta = csc^2 theta

3. Angle Sum and Difference Formulas
sin(A + B) = sin A cos B + cos A sin B
sin(A - B) = sin A cos B - cos A sin B
cos(A + B) = cos A cos B - sin A sin B
cos(A - B) = cos A cos B + sin A sin B
tan(A + B) = (tan A + tan B)/(1 - tan A tan B)
tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

4. Double Angle Formulas
sin 2A = 2 sin A cos A
cos 2A = cos^2 A - sin^2 A = 2 cos^2 A - 1 = 1 - 2 sin^2 A
tan 2A = 2 tan A / (1 - tan^2 A)

5. Half Angle Formulas
sin^2(A/2) = (1 - cos A)/2
cos^2(A/2) = (1 + cos A)/2
tan(A/2) = (1 - cos A)/sin A = sin A / (1 + cos A)

6. Product to Sum Formulas
sin A sin B = 1/2 [cos(A - B) - cos(A + B)]