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2018-12-02

Who discovered math theorems in geometry?

Who discovered math theorems in geometry?

Pythagoras of Samos

What is Pythagorean theorem identity?

The Pythagorean identity tells us that no matter what the value of θ is, sin²θ+cos²θ is equal to 1. This follows from the Pythagorean theorem, which is why it’s called the Pythagorean identity! We can use this identity to solve various problems.

What is the difference between Pythagorean theorem and trigonometry?

There is a vast difference between these two. Trigonometry is a branch of Mathematics which deals with length and angles. Whereas, Pythagoras theorem is a law or formulae used in finding length in a right angled triangle involved in trigonometry.

Can trig equations have no solution?

since it is assumed as part of the solution to any trigonometric equation. Because the set of values from 0 to 2Π contains the domain for all six trigonometric functions, if there is no solution to an equation between these bounds, then no solution exists.

Why do trig equations have an infinite number of solutions?

Because of the periodic nature of the trigonometric functions – they repeat themselves infinitely many times – the variable x can take on an infinite number of solutions.

Why does Sinx 2 have no solution?

The range of sine is −1≤y≤1 – 1 ≤ y ≤ 1 . Since 2 does not fall in this range, there is no solution.

Do all trigonometric equations have an infinite number of solutions?

Not all trigonometric equations have an infinite number of solutions. For example, cosx=73 has no solutions. cosx=kx has a finite number of solutions (except for k=0) whose number depends on k. For example, cosx=110x has 7 solutions.

Does an identity have an infinite number of solutions?

If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions and is called an identity. So, the equation is an identity and has infinitely many solutions.

How do we find the solution of a trigonometric equation if it has only one term?

If a trig equation can be solved analytically, these steps will do it:

  1. Put the equation in terms of one function of one angle.
  2. Write the equation as one trig function of an angle equals a constant.
  3. Write down the possible value(s) for the angle.
  4. If necessary, solve for the variable.

How do you find the number of solutions in a trig equation?

First try to find the solutions over R, then select those which in [0,2π]. Set t=tanx2(x≢πmod2π). The restriction on the values of x is unimportant, as one checks these values are no solutions of the equation. We know that cosx=1−t21+t2,sinx=2t1+t2.

What is the formula of general solution?

Trigonometric Equations with their general Solutions:

Trigonometrical equation General Solution
cos θ = 0 θ = (nπ + π/2)
tan θ = 0 θ = nπ
sin θ = 1 θ = (2nπ + π/2) = (4n+1)π/2
cos θ = 1 θ = 2nπ

How do you find the general value?

Find the most general value of theta satisfyingn the equation tantheta=-1 and costheta=(1 )/(sqrt(2)). Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Hence, the most general value of θ i.e., θ=2nπ+7π4.

What are the trigonometric equations?

Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. It is expressed as ratios of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.

What Sinx 0?

sinx is known as a periodic function that oscillates at regular intervals. It crosses the x-axis (i.e. it is 0 ) at x=0,π, and 2π in the domain [0,2π] , and continues to cross the x-axis at every integer multiple of π .

What are the three trigonometric equations?

The three main functions in trigonometry are Sine, Cosine and Tangent.