Introduction to Trigonometry – Formula & Equation Sheet
Essential formulas and equations from Mathematic, tailored for Class 10 in Mathematics.
This one-pager compiles key formulas and equations from the Introduction to Trigonometry chapter of Mathematic. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
sin A = opposite / hypotenuse
sin A represents the sine of angle A; 'opposite' is the length of the side opposite angle A, and 'hypotenuse' is the length of the triangle's hypotenuse. Used to find angles or sides in right triangles.
cos A = adjacent / hypotenuse
cos A represents the cosine of angle A; 'adjacent' is the length of the side adjacent to angle A. Utilized in determining angles or distances in right triangle contexts.
tan A = opposite / adjacent
tan A denotes the tangent of angle A; it compares the lengths of the opposite and adjacent sides. Important for calculating angles when two sides are known.
cosec A = 1 / sin A
cosec A denotes the cosecant of angle A, equal to the reciprocal of sine. This is helpful in solving for angles or sides when using sine.
sec A = 1 / cos A
sec A represents the secant of angle A, equal to the reciprocal of cosine. Often used in triangles where cosine values are needed.
cot A = 1 / tan A
cot A defines the cotangent of angle A, the reciprocal of tangent. Useful for converting between trigonometric functions.
sin² A + cos² A = 1
This identity shows the fundamental relationship between sine and cosine. It is a cornerstone in trigonometry, helping solve for unknown functions.
tan A = sin A / cos A
This equation shows that tangent can be expressed as the ratio of sine to cosine. It helps in evaluating tangent when sine and cosine are known.
sin(90° - A) = cos A
This co-function identity indicates that the sine of an angle complements the cosine of its complement. It's crucial for solving problems with complementary angles.
tan(90° - A) = cot A
This identity demonstrates how tangent relates to cotangent for complementary angles, aiding in solving problems with complementary angles.
Equations
Pythagoras Theorem: a² + b² = c²
This theorem relates the lengths of the sides of a right triangle, where 'c' is the hypotenuse and 'a' and 'b' are the other two sides. Fundamental for finding unknown lengths.
sin A = 4/5 implies cos A = 3/5
Using the identity sin² A + cos² A = 1 to derive cos A from a known sin A value. Used frequently in angle and side calculations.
cot A = 1/tan A
Defines cotangent as the reciprocal of tangent. Helpful in angle transformations and calculations.
sin(45°) = cos(45°) = 1/√2
Both sine and cosine of 45 degrees are equal, which helps in solving trigonometric problems involving 45-degree angles.
sin(30°) = 1/2, cos(30°) = √3/2
These specific values are derived from the geometry of a 30-60-90 triangle, critical for quick calculations in trigonometry.
tan(30°) = 1/√3
The ratio is derived from a 30-60-90 triangle. This value assists in solving for angles or sides in related problems.
sin(60°) = √3/2, cos(60°) = 1/2
Specific values from the geometry of a 30-60-90 triangle, useful for quick reference in calculations.
tan(45°) = 1
The tangent of 45 degrees equals one, indicating equal sides in an isosceles right triangle, fundamental for geometric proofs.
sin(90°) = 1, cos(90°) = 0
Defines the behavior of sine and cosine at 90 degrees. Essential for accuracy in angle calculations.
tan(90°) is undefined
Indicates that the tangent function approaches infinity as angle A approaches 90 degrees, critical for understanding asymptotic behavior.
