Trigonometric Function Formulas

You know that we have Hypotenuse – the longest side Base – the third side Perpendicular – the other side opp to the angle in a right triangle Similarly, the six trigonometric functions are: Sine Cosine Secant Cosecant Tangent Cotangent Now let’s study the basic trigonometry formulas. The Trigonometric properties/Formulas are given below: Property Identity / Property Mathematical value Sin a opposite/hypotenuse Cos a adjacent/hypotenuse Tan a opposite/adjacent sina/cosa Sec a hypotenuse/adjacent 1/cosa Cosec a hypotenuse/opposite 1/sina Cot a adjacent/opposite cosa/sina=1/tana

Tangent 3 Theta Formula

The relationship between the basic trigonometric functions taking 3 times the angle in the trigonometric functions of those angles itself, gives The trigonometric triple-angle identities. You can either expand or simplify the triple angle tan functions like tan 3 A, tan 3 x, tan 3 alpha, etc by using triple angle identity. Tan 3 theta = 3 tan theta – tan 3 theta / 1 – 3 tan2 theta Where tan is a tangent function and theta is an angle. This is one of the important trigonometry formulas. Tan 3x Formula Example: Question: Find the…

Tan Theta formula

The law of Tangent which is also called a tangent formula or tangent rule is the ratio of the sine of the angle to the cos of the angle. Tan Θ = Opposite / Adjacent Tan x formula The Tan Θ is the ratio of the Opposite side to the Adjacent, where (Θ) is one of the acute angles. \(Tan \Theta = \frac{Opposite}{Adjacent}\) Tan alpha Questions Out of the other 6 trigonometric formulas, let’s have a look at the practice question of tan theta formula. Example 1: If Sin x =…

Tan2x Formula

Sin 2x, Cos 2x, Tan 2x is the trigonometric formulas which are called as double angle formulas because they have double angles in their trigonometric functions. Let’s understand it by practicing it through solved example. Tan2x=2tanx/1−tan2x Introduction to Tan double angle formula let’s look at trigonometric formulae also called as the double angle formulae having double angles Derive Double Angle Formulae for Tan 2 Theta Tan2x=2tanx/1−tan2x let’s recall the addition formula. tan(a+b)=tana+tanb/1−tana.tanb So, for this let a = b, it becomes tan(a+a)=tana+tana/1−tana.tana Tan2a=2tana/1−tan2a Practice Example for Tan2 theta: Question: Find Tan2x, if tan…

Sin Theta Formula

The right triangle formulas are the most important ones in the trigonometry. The sin Theta is the ratio of the opposite side to the hypotenuse, If theta (Θ) is one of the acute angles. Sin x Formula: It is one of the formulae of the Sin function from the six other trigonometric functions. Sin Θ = OppositeSide/Hypotenuse Sin angle Questions Example: If cos x = 4/5, Find the value of Sin x? Solution: Using Trigonometric identities: Sin2x = 1- Cos2x Sin2x = 1 – (4/5)2 = 1 – 16/25 = (25 – 16) / 25 =…

Cos Inverse Formula

Cos Inverse is also written as Arccos and Cos-1 and is called an anti trigonometric function. The cos inverse is an inverse trigonometric function with restricted domains. The Cos inverse Formula is : Arccos Questions The cos inverse formula is one amongst the other six inverse trigonometric functions. Question: Find the exact Value of Arccos(-½) Solution: arccos(- 1 / 2) Assume y = arccos(- 1 / 2). cos y = – 1 / 2 with 0 ≤ y ≤ Π (Cos Theorem) … (1) Cos (π / 3) = 1 / 2…

Sin Cos Formulas

Sin and Cos are basic trigonometric functions that tell about the shape of a right triangle, so the Sin Cos formulas are the basic ones in trigonometry. Sin A = Perpendicular/Hypotenuse Cos A = Base/Hypotenuse Basic Trigonometric Identities for Sine and Cos These formulas help in giving a name to each side of the right triangle and these are also used in trigonometric formulas for class 11. Let’s learn the basic sin and cos formulas. cos2(A) + sin2(A) = 1 If A + B = 180° then: sin(A) = sin(B) cos(A) = -cos(B)…