Trigonometry Formula Cheat Sheet with Identities Guide

Trigonometry formula cheat sheet provides key trig identities, angle formulas, and sine cosine tangent values, making it simple to solve triangle problems and understand angle relationships in mathematics.

Trigonometry Formula Cheat Sheet

Topic	Formula	Description
Sine Ratio	sinθ = Opp/Hyp	Opposite over hypotenuse
Cosine Ratio	cosθ = Adj/Hyp	Adjacent over hypotenuse
Tangent Ratio	tanθ = Opp/Adj	Opposite over adjacent
Cotangent	cotθ = Adj/Opp	Reciprocal of tan
Secant	secθ = 1/cosθ	Reciprocal of cos
Cosecant	cscθ = 1/sinθ	Reciprocal of sin
Pythagorean Identity	sin²θ + cos²θ = 1	Basic identity
Identity	1 + tan²θ = sec²θ	Relation
Identity	1 + cot²θ = csc²θ	Relation
tanθ	sinθ / cosθ	Ratio form
cotθ	cosθ / sinθ	Ratio form
Complementary	sin(90°−θ) = cosθ	Co-function
Complementary	cos(90°−θ) = sinθ	Co-function
Complementary	tan(90°−θ) = cotθ	Co-function
Sum Formula	sin(A+B) = sinAcosB + cosAsinB	Angle addition
Difference Formula	sin(A−B) = sinAcosB − cosAsinB	Angle subtraction
Cosine Formula	cos(A+B) = cosAcosB − sinAsinB	Addition
Cosine Formula	cos(A−B) = cosAcosB + sinAsinB	Subtraction
Tangent Formula	tan(A+B) = (tanA + tanB)/(1 − tanAtanB)	Addition
Tangent Formula	tan(A−B) = (tanA − tanB)/(1 + tanAtanB)	Subtraction
Double Angle	sin2θ = 2sinθcosθ	Double angle
Double Angle	cos2θ = cos²θ − sin²θ	Double angle
Double Angle	tan2θ = 2tanθ/(1 − tan²θ)	Double angle
Half Angle	sin²(θ/2) = (1 − cosθ)/2	Half angle
Half Angle	cos²(θ/2) = (1 + cosθ)/2	Half angle
Degree to Radian	θ × (π/180)	Conversion
Radian to Degree	θ × (180/π)	Conversion
Law of Sines	a/sinA = b/sinB = c/sinC	Triangle relation
Law of Cosines	c² = a² + b² − 2ab cosC	Triangle rule
Area of Triangle	(1/2)ab sinC	Using trig
Special Values	sin0°=0, sin30°=1/2, sin45°=1/√2, sin60°=√3/2, sin90°=1	Standard values
Special Values	cos0°=1, cos30°=√3/2, cos45°=1/√2, cos60°=1/2, cos90°=0	Standard values
Special Values	tan0°=0, tan30°=1/√3, tan45°=1, tan60°=√3, tan90°=∞	Standard values

Download PDF

Conclusion Trigonometry is a mathematical field that deals with the correlation amid angles and sides of triangles, particularly right-angled triangles. It presents the functions sine, cosine and tangent, which are applied in solving problems with angles and distances. Applications in engineering, physics, astronomy and navigation are common in trigonometry. It assists in the determination of heights, distances and angles which are hard to determine directly. Periodic patterns are easier to comprehend with the help of concepts such as trigonometric identities, equations, and graphs. Another major area that trigonometry is used is in wave analysis, sound, and light. Trigonometry can be learnt to enhance analytical thinking and to solve real-life problems that involve angles. It finds application in computer graphics, construction and surveying as well. With the knowledge of trigonometric ratios and formulas, students will be able to make complex calculations easy. Trigonometry bridges geometry and algebra, and is the foundation of higher-level sciences such as calculus. On the whole, it is a useful mathematical instrument that can be used to comprehend the relationships among angles and distances. In conclusion, trigonometry is essential for solving problems involving angles and measurements. It is widely used in science and engineering and strengthens problem-solving skills.