What are Trigonometric Functions Formulas

About Trigonometric Functions

What are Trigonometric Functions?

There are six trigonometric functions used in Trigo. These six basic trig functions are sine, cosine, secant, co-secant, tangent, and co-tangent functions. Trigonometric functions and identities are ratios of sides of a right-angled triangle. The sides of a right triangle are perpendicular, hypotenuse and base, which are used to evaluate sin, cos, tan, cosec, sec and cot values using trigonometric formulas.

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Trigonometric Functions Formulas

We have certain formulas to evaluate values of Trigo functions using the sides of a right-angled triangle. To write these formulas, we use the abbreviated form of these functions. Sine is denoted by sin, cosine is denoted by cos, the tangent is abbreviated as tan, secant is abbreviated as a sec, cosecant is denoted by cosec, and cotangent is denoted by the cot. The basic formulas to find trigonometric functions are as follows:

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As we can observe from the above-given formulas, sin and cosec are reciprocals of each other. Similarly, reciprocal pairs are cos and secant, and tan and cot.

Trigonometric Functions Values

Trigonometric functions have a domain θ, which is in degree or radian. Some of the principal values of θ for different trigonometric functions are represented below in the table. These principal values are also represented as standard values of Trigo functions at specific angles and are frequently used in evaluations. The principal value of Trigo functions has been derived from a unit circle. These values also satisfy all the Trigo formulas.

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Trigo Functions in Four Quadrants

Angle θ is an acute angle which is measured concerning the positive x-axis in the anticlockwise direction. These trigo functions have different numeric signs (+ or -) in the different quadrants, that is based on the positive or negative axis of the quadrant. Here, Sinθ, and Cosecθ are positive in quadrants I and II, while it’s negative in quadrants III and IV. All trigonometric functions have a positive range in the first quadrant. Here, tanθ, and cotθ are positive only in Quadrants I and III, and the trigonometric ratios of Cosθ and Secθ are positive only in quadrants I and IV.

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Trigonometric functions have values of θ, (90° - θ) in the first quadrant. Co-function identities provide interrelationships between different complementary Trigo functions for angle (90° - θ).

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Domain θ value for different Trigo functions in the second quadrant is (π/2 + θ, π - θ), in the third quadrant is (π + θ, 3π/2 - θ), and in the fourth quadrant is (3π/2 + θ, 2π - θ). For π/2, 3π/2 trigonometric values changes as their complementary ratios such as Sinθ⇔Cosθ, Tanθ⇔Cotθ, Secθ⇔Cosecθ. For π, 2π trigonometric values remain the same. Changing Trigo ratios in different quadrants and angles can be understood from the below table.

Trigonometric