Explore the basics of trigonometry, including angles, triangles, and the fundamental trigonometric ratios: sine, cosine, and tangent.
Introduction to Trigonometry – Formula & Equation Sheet
Essential formulas and equations from Mathematics, tailored for Class X in Mathematics.
This one-pager compiles key formulas and equations from the Introduction to Trigonometry chapter of Mathematics. 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, where 'opposite' is the length of the side opposite to angle A and 'hypotenuse' is the length of the longest side in the right triangle. Used to find the ratio of the opposite side to the hypotenuse.
cos A = adjacent/hypotenuse
cos A represents the cosine of angle A, where 'adjacent' is the length of the side adjacent to angle A. Used to find the ratio of the adjacent side to the hypotenuse.
tan A = opposite/adjacent
tan A represents the tangent of angle A. It is the ratio of the sine of angle A to the cosine of angle A. Useful for finding the slope in geometry.
cosec A = 1/sin A
cosec A is the cosecant of angle A, the reciprocal of sin A. Used in trigonometric identities and equations.
sec A = 1/cos A
sec A is the secant of angle A, the reciprocal of cos A. Important in trigonometric functions and identities.
cot A = 1/tan A
cot A is the cotangent of angle A, the reciprocal of tan A. Used in various trigonometric calculations.
sin² A + cos² A = 1
This is the Pythagorean identity, showing the fundamental relation between sin A and cos A in a right triangle.
1 + tan² A = sec² A
Derived from the Pythagorean identity, this relation connects tan A and sec A. Useful in trigonometric proofs and problems.
1 + cot² A = cosec² A
Another Pythagorean identity variant, linking cot A and cosec A. Essential for solving trigonometric equations.
tan A = sin A / cos A
Shows the relationship between tan A, sin A, and cos A. Useful for converting between trigonometric functions.
Equations
sin 30° = 1/2
The sine of 30 degrees is 1/2. This is a standard value used in solving problems involving right triangles with a 30° angle.
cos 45° = 1/√2
The cosine of 45 degrees is 1 divided by the square root of 2. A key value for isosceles right triangles.
tan 60° = √3
The tangent of 60 degrees is the square root of 3. Important for equilateral triangles split into two right triangles.
sin 0° = 0
The sine of 0 degrees is 0, indicating no opposite side in a right triangle at this angle.
cos 90° = 0
The cosine of 90 degrees is 0, showing no adjacent side in a right triangle at this angle.
tan 45° = 1
The tangent of 45 degrees is 1, meaning the opposite and adjacent sides are equal in length.
cosec 30° = 2
The cosecant of 30 degrees is 2, the reciprocal of sin 30°. Useful in trigonometric calculations.
sec 60° = 2
The secant of 60 degrees is 2, the reciprocal of cos 60°. Important for solving trigonometric problems.
cot 45° = 1
The cotangent of 45 degrees is 1, the reciprocal of tan 45°. Used in various trigonometric identities.
sin (90° - A) = cos A
This identity shows the complementary relationship between sine and cosine functions. Essential for angle transformation.
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