How do you find the general solution of a trigonometric equation?
Table of Contents
- 1 How do you find the general solution of a trigonometric equation?
- 2 How do you solve sin x cos x?
- 3 What is the general solution of sin?
- 4 What is general solution in trigonometry?
- 5 What is cos sin equal to?
- 6 What is the general solution for sin x = 0?
- 7 How do you find the solution of sin(π -θ) and cos(-θ)?
How do you find the general solution of a trigonometric equation?
are solutions of the given equation. Hence, the general solution for sin x = 0 will be, x = nπ, where n∈I….Solutions for Trigonometric Equations.
| Equations | Solutions |
|---|---|
| sin x = 1 | x = (2nπ + π/2) = (4n+1)π/2 |
| cos x = 1 | x = 2nπ |
| sin x = sin θ | x = nπ + (-1)nθ, where θ ∈ [-π/2, π/2] |
| cos x = cos θ | x = 2nπ ± θ, where θ ∈ (0, π] |
What is the general solution of Sinx COSX?
General solution of sinx=cosx is x=nπ+π4 , where n is an integer.
How do you solve sin x cos x?
The equation sin x = cos x can also be solved by dividing through by cos x. If we put k = 0 and k = 1 we get the solutions /4 (45°) and /4 + = 5 /4 (45°+ 180°= 225°). To solve the inequality sin x > cos x we need to see which is the greater sin x or cos x on the intervals between the solutions /4 and 5 /4.
Is Sinx COSX 1 true?
Because sin(2x)≤1 for all x∈R (for all real-valued x ) that means that cos(x)sin(x)≤12 for all real x .
What is the general solution of sin?
Trigonometrical equations with their general solution
| Trigonometrical equation | General solution |
|---|---|
| sin θ = sin α | θ = nπ + (−1)nα |
| cos θ = cos α | θ = 2nπ ± α |
| tan θ = tan α | θ = nπ ± α |
| sin2 θ = sin2 α | θ = nπ ± α |
What is a general solution in trigonometry?
The general solution (EMCGJ) The periodicity of the trigonometric functions means that there are an infinite number of positive and negative angles that satisfy an equation. We know that the sine and cosine functions have a period of 360° and the tangent function has a period of 180°.
What is general solution in trigonometry?
Hint: Trigonometric equations involve functions like sin, cos, tan, cosec, sec and cot. After solving these equations we will get some values and all these values which involves integer n is our general solution. The equations which involve trigonometric functions like sin, cos, tan, cot, sec etc.
What is Sinx divided by COSX?
The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x .
What is cos sin equal to?
Sine, Cosine and Tangent
| Sine Function: | sin(θ) = Opposite / Hypotenuse |
|---|---|
| Cosine Function: | cos(θ) = Adjacent / Hypotenuse |
| Tangent Function: | tan(θ) = Opposite / Adjacent |
What is the general solution of the Trigonometrical equation?
Trigonometrical equations with their general solution Trigonometrical equation General solution sin θ = 0 θ = nπ cos θ = 0 θ = nπ + π/2 tan θ = 0 θ = nπ sin θ = 1 θ = 2nπ + π/2
What is the general solution for sin x = 0?
But, we know that if sin x = 0, then x = 0, π, 2π, π, -2π, -6π, etc. are solutions of the given equation. Hence general solution for sin x = 0 will be, x = nπ, where n∈I.
What is cos x -sin2x = 0?
For example, cos x -sin 2 x = 0, is a trigonometric equation which does not satisfy all the values of x. Hence for such equations, we have to find the values of x or find the solution. We know that sin x and cos x repeat themselves after an interval of 2π, and tan x repeats itself after an interval of π.
How do you find the solution of sin(π -θ) and cos(-θ)?
From the following diagram we see that sin (π -θ) = sin θ and cos ( -θ) = cos θ. We use this to find the solutions of some trig equations. Solve sin (x) = y for x. Case 1: -1≤ y ≤ 1, that is, the value of y is between -1 and 1, so there is a solution.