Below is the table for trigonometry formulas for angles that are commonly used for solving problems. Angles (In Degrees) 0° 30° 45° 60° 90° 180° 270° 360° Angles (In Radians) 0 π/6 π/4 π/3 π/2 π 3π/2 2π sin 0 1/2 1/√2 √3/2 1 0 -1 0 cos 1 √3/2 1/√2 1/2 0 -1 0… Continue reading Trigonometry Table
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Reciprocal Identities
The Reciprocal Identities are given as: cosec θ = 1/sin θ sec θ = 1/cos θ cot θ = 1/tan θ sin θ = 1/cosec θ cos θ = 1/sec θ tan θ = 1/cot θ All these are taken from a right-angled triangle. When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the… Continue reading Reciprocal Identities
Basic Function Formulas
There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent. By using a right-angled triangle as a reference, the trigonometric functions and identities are derived: sin θ = Opposite Side/Hypotenuse cos θ = Adjacent Side/Hypotenuse tan θ = Opposite Side/Adjacent Side sec… Continue reading Basic Function Formulas
JEE Main Maths Trig Previous Year Questions With Sol.
Question 1: The general solution of sin x − 3 sin2x + sin3x = cos x − 3 cos2x + cos3x is _________. Solution: sinx − 3 sin2x + sin3x = cosx − 3 cos2x + cos3x ⇒ 2 sin2x cosx − 3 sin2x − 2 cos2x cosx + 3 cos2x = 0 ⇒ sin2x (2cosx… Continue reading JEE Main Maths Trig Previous Year Questions With Sol.
Trigonometric Functions: Even, Odd Or Neither
What Is An Even Function? An even function is symmetric (by reflection) about the y-axis , i.e.f(-x) = f(x) What Is An Odd Function? An odd function is symmetric (by 180° rotation) about the origin, i.e.f(-x) = -f(x) The following table shows the Even Trigonometric Functions and Odd Trigonometric Functions. Scroll down the page for… Continue reading Trigonometric Functions: Even, Odd Or Neither
Solving Trigonometric Equations
Unlike normal solutions of algebraic equations with the number of solutions based on the degree of the variable, in trigonometric equations, the solutions are of two types, based on the different value of angle for the trigonometric function, for the same solution. For example, for a simple trigonometric equation 2Cosθ – 1 = 0, the solution… Continue reading Solving Trigonometric Equations
Trig. Equations Formulas
We use some results and general solutions of the basic trigonometric equations to solve other trigonometric equations. These results are as follows: For any real numbers x and y, sin x = sin y implies x = nπ + (-1)ny, where n ∈ Z. For any real numbers x and y, cos x = cos… Continue reading Trig. Equations Formulas
Trigonometric Equations
The trigonometric equations involve trigonometric functions of angles as variables. The angle of θ trigonometric functions such as Sinθ, Cosθ, Tanθ is used as a variable in trigonometric equations. Similar to general polynomial equations, the trigonometric equations also have solutions, which are referred to as principal solutions, and general solutions. We will use the fact that the… Continue reading Trigonometric Equations
Double‐Angle and Half‐Angle Identities
Special cases of the sum and difference formulas for sine and cosine yields what is known as the double‐angle identities and the half‐angle identities. First, using the sum identity for the sine, sin 2α = sin (α + α) sin 2α = sin α cos α + cos α sin α sin 2α = 2 sin α cos… Continue reading Double‐Angle and Half‐Angle Identities
Sum And Difference Identities
In these lessons we will learn the sum identities and difference identities for sine, cosine and tangent. how to use the sum identities and difference identities to simplify trigonometric expressions. how to use the sum identities and difference identities to prove other trigonometric identities. What are the Sum and Difference Identities? The following shows the… Continue reading Sum And Difference Identities