Formula Sheet: Trigonometric Functions
This chapter introduces trigonometric functions, explaining their definitions, properties, and applications. Understanding these concepts is essential for solving various mathematical problems and real-world applications.
Trigonometric Functions – Formula & Equation Sheet
Essential formulas and equations from Mathematics, tailored for Class 11 in Mathematics.
This one-pager compiles key formulas and equations from the Trigonometric Functions chapter of Mathematics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formula sheet
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
sin²x + cos²x = 1
This identity relates the sine and cosine of an angle x. It is fundamental in trigonometry, illustrating the Pythagorean theorem and that for any angle x, the square of sine plus the square of cosine equals one.
1 + tan²x = sec²x
This identity connects tangent and secant functions. It is useful in solving equations and simplifying expressions involving tangent.
1 + cot²x = csc²x
This identity relates cotangent and cosecant functions. It's essential for converting between different trigonometric identities.
cos(x + y) = cos x cos y - sin x sin y
This formula expresses the cosine of a sum of two angles in terms of the cosine and sine of each angle. Useful in simplifying expressions involving angles.
cos(x - y) = cos x cos y + sin x sin y
This formula addresses the cosine of the difference between two angles. It helps in calculations involving angle differences.
sin(x + y) = sin x cos y + cos x sin y
This identity represents the sine of a sum of two angles in terms of the sine and cosine of each angle.
sin(x - y) = sin x cos y - cos x sin y
Similar to the sum formula, it provides an expression for the sine of the difference of two angles.
sin 2x = 2 sin x cos x
This double angle formula for sine expresses sin of double an angle in terms of sine and cosine of the angle itself.
cos 2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x
This formula helps to find cosine of double an angle using either sine, cosine, or both.
tan 2x = (2tan x) / (1 - tan²x)
This double angle formula for tangent provides a way to compute the tangent of double an angle based on the tangent of the angle itself.
Equations
l = rθ
This formula gives the arc length l of a circle based on the radius r and the angle θ in radians. It is fundamental for problems involving circular motion.
θ = arcsin(x)/sin^-1(x), θ = arccos(x)/cos^-1(x), θ = arctan(x)/tan^-1(x)
These functions (inverse sine, cosine, and tangent) give the angle corresponding to a given sine, cosine, or tangent value, respectively.
l = r(π/180) * degrees
This conversion formula relates the angle in degrees to radians when calculating arc length in circular motion.
cot x = 1/tan x
This defines cotangent as the reciprocal of tangent, useful for transforming equations involving trigonometric functions.
cosec x = 1/sin x
This defines cosecant as the reciprocal of sine, essential for transforming among trigonometric identities.
sec x = 1/cos x
This defines secant as the reciprocal of cosine, facilitating conversions and manipulations of trigonometric expressions.
sin(-x) = -sin x
This property shows that the sine function is odd, relevant in symmetry aspects of trigonometric graphs.
cos(-x) = cos x
This property highlights that the cosine function is even, simplifying calculations for negative angles.
tan(-x) = -tan x
This indicates the odd property of the tangent function, necessary for understanding the behavior of tangent functions.
cot(-x) = -cot x
Similar to tangent, this indicates cotangent’s odd behavior, useful for various trigonometric applications.
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