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
Month: September 2022
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
Sine and Cosine Rule Trig Identities
The sine rule gives the relation between the angles and the corresponding sides of a triangle. For the non-right-angled triangles, we will have to use the sine rule and the cosine rule. For a triangle with sides ‘a’, ‘b’, and ‘c’ and the respective opposite angles are A, B, and C, sine rule can be given as,… Continue reading Sine and Cosine Rule Trig Identities
What are Trigonometric Identities?
Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain. Basically, an identity is an equation that holds true for all the values of the variable(s) present in it. For example, some of the algebraic identities are:(a + b)2 = a2 + 2ab + b2(a… Continue reading What are Trigonometric Identities?
Trigonometric Identities
Trigonometric identities (trig identities) are equalities that involve trigonometric functions that are true for all values of the occurring variables. These identities are useful when we need to simplify expressions involving trigonometric functions. The following is a list of useful Trigonometric identities: Quotient Identities, Reciprocal Identities, Pythagorean Identities, Co-function Identities, Addition Formulas, Subtraction Formulas, Double… Continue reading Trigonometric Identities
Transformation Of Trig Graphs
In these lessons, we will learn how Trigonometric Graphs can be transformed the amplitude and vertical shift of Trigonometric Graphs the period and phase shift of Trigonometric Graphs The following diagrams show how to determine the transformation of a Trigonometric Graph from its equation. Scroll down the page for more examples and solutions. Amplitude Of… Continue reading Transformation Of Trig Graphs
Tangent, Cotangent, Secant, Cosecant Graphs
The following diagram shows the tangent and cotangent graphs. Scroll down the page for more examples and solutions about Tangent, Cotangent, Secant, Cosecant graphs.