Trigonometric formulae

Trigonometry formulae are asked in various types of Exams like CBSE boards exam/ICSE Boards exams/State board exams,Class 10/ class 11 and many more.

Trigonometry formulae plays very important role ,if you memories these formulae very well you can solve many Questions based on trigonometry formulae so here we are Providing the list of trigonometry formulas.

What are the basic trigonometric functions?

The basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

How are trigonometric ratios defined in a right triangle?

Trigonometric ratios in a right triangle are defined as follows:
Sinθ = Opposite side / Hypotenuse
Cosθ = Adjacent side / Hypotenuse
Tanθ = Opposite side / Adjacent side
Cscθ = 1 / Sinθ
Secθ = 1 / Cosθ
Cotθ = 1 / Tanθ

What is the Pythagorean trigonometric identity?

The Pythagorean trigonometric identity is: Sin²θ + Cos²θ = 1

How do you convert between radians and degrees?

To convert radians to degrees, multiply by (180/π). To convert degrees to radians, multiply by (π/180)

What are the sum and difference formulas for sine and cosine?

The sum and difference formulas are:
Sin(A ± B) = SinA * CosB ± CosA * SinB
Cos(A ± B) = CosA * CosB ∓ SinA * SinB

What is the double-angle formula for sine?

The double-angle formula for sine is: Sin(2θ) = 2 * Sinθ * Cosθ

What are the half-angle formulas for trigonometric functions?

The half-angle formulas are:
Sin(θ/2) = ± √[(1 – Cosθ) / 2]
Cos(θ/2) = ± √[(1 + Cosθ) / 2]
Tan(θ/2) = ± √[(1 – Cosθ) / (1 + Cosθ)]

How do you find the trigonometric values of special angles?

Trigonometric values of special angles (0°, 30°, 45°, 60°, 90°) can be determined using reference triangles or the unit circle.

What is the law of sines and how is it used?

The law of sines states: (SinA / a) = (SinB / b) = (SinC / c), where A, B, C are angles and a, b, c are corresponding sides in a triangle. It’s used to solve triangles when given angle-side-angle or side-angle-side.

What is the law of cosines and how is it applied?

The law of cosines is: c² = a² + b² – 2ab * CosC. It’s used to solve triangles when given side-side-side (SSS), side-angle-side (SAS), or angle-side-angle (ASA).

What are the trigonometric identities for tangent and cotangent?

The trigonometric identities are:
Tanθ = Sinθ / Cosθ
Cotθ = Cosθ / Sinθ

How are trigonometric functions used in real-world applications?

Trigonometric functions are used in fields like engineering, physics, astronomy, and navigation for calculating distances, angles, waves, and more.

What is the relationship between trigonometric functions and the unit circle?

Trigonometric functions are related to the unit circle by the coordinates (Cosθ, Sinθ) for any angle θ.

How do you prove trigonometric identities?

Trigonometric identities are proven using algebraic manipulations, substitution, and applying known trigonometric relationships.

What are the inverse trigonometric functions and their properties?

Inverse trigonometric functions (Arcsin, Arccos, Arctan, Arccsc, Arcsec, Arccot) return angles corresponding to given ratios, with specific domains and ranges to ensure uniqueness of solutions.

What are the derivatives of trigonometric functions?

The derivatives of trigonometric functions are used in calculus to find rates of change and slopes of trigonometric curves.

How do you integrate trigonometric functions?

Trigonometric functions can be integrated using techniques like substitution, integration by parts, and trigonometric identities.

How do you solve triangles using trigonometric ratios?

Triangles can be solved using trigonometric ratios such as sine, cosine, and tangent, based on the lengths of sides and measures of angles.

What is the general solution of a trigonometric equation?

The general solution of a trigonometric equation includes all possible solutions within a specified interval, taking into account periodicity of trigonometric functions.

Trigonometry formulae are very crucial topic in Mathematics when it comes to asked questions on the topic “Trigonometric formulae”:

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