Trignometric identities question

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In summary, the conversation discusses solving a goniometric equation by replacing sin(x) with a variable, p, and then solving the resulting quadratic equation. However, there is a mistake in the process as the expression 2p^2+ p is not equivalent to 2(1-cos^2)+cos^2. It is recommended to instead solve the equation using the quadratic formula, with p as the variable, and then substituting the solutions back in for sin(x).
  • #1
tempeste
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Hi,

the question is

2sin^2 + sinX -1 = 0

I think the next step is then

2(1-cos^2)+cos^2=0

Did I do something wrong because I cannot seem to continue the question?
 
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  • #2
Just replace sin(x) by a variable p.
the equations then is 2p² + p - 1 = 0

Solve this equation for p and then set these solutions equal to sin(x)
At best you will have two goniometric equations to solve

marlon
 
  • #3
tempeste said:
Hi,

the question is

2sin^2 + sinX -1 = 0

I think the next step is then

2(1-cos^2)+cos^2=0

Did I do something wrong because I cannot seem to continue the question?

Yes,i've colored in red what is wrong,namely
[tex] \sin x -1=\cos^{2} x [/tex]

That is wrong...As an indentity.It is valid as an equation in "x",which,i'm afraid,is not really equivalent to your initial one...

Daniel.
 
  • #4
I still don't really understand...

I tried it marlon's way

2p^2+p-1=0
2p^2+p=1
2p+p=1 (squareroot)
3p=1
p=1/3

Is the right?
 
  • #5
tempeste said:
I still don't really understand...

I tried it marlon's way

2p^2+p-1=0
2p^2+p=1
2p+p=1 (squareroot)
3p=1
p=1/3

Is the right?

Not at all.

Can you solve an equation like ax² + bx + c = 0 ?
Discriminant D = b² -4ac

first solution = [tex]\frac{-b + \sqrt{D}}{2a}[/tex]
second solution = [tex]\frac{-b - \sqrt{D}}{2a}[/tex]

Just apply this to your equation where x is now p

marlon
 
  • #6
No, it isn't.

square root of 2p^2+ p is NOT 2p+ p!

Can you factor 2p^2+ p- 1?
 

FAQ: Trignometric identities question

1. What are trigonometric identities?

Trigonometric identities are mathematical equations that involve the trigonometric functions (sine, cosine, tangent, etc.) and are true for all values of the variables. They are used to simplify and manipulate trigonometric expressions and equations.

2. What is the difference between a trigonometric identity and a trigonometric equation?

A trigonometric identity is an equation that is true for all values of the variables, while a trigonometric equation is an equation that is only true for specific values of the variables. Trigonometric identities are used to prove or simplify equations, while trigonometric equations are used to solve for specific values.

3. How do you verify a trigonometric identity?

To verify a trigonometric identity, you need to show that it holds true for all values of the variables. This can be done by simplifying both sides of the equation using algebraic manipulations and the properties of trigonometric functions.

4. What are the most commonly used trigonometric identities?

Some of the most commonly used trigonometric identities include the Pythagorean identities, double angle identities, half angle identities, and sum and difference identities.

5. How are trigonometric identities used in real life?

Trigonometric identities have various real-life applications, such as in navigation, engineering, and physics. They are also used in computer graphics and animation to create realistic and accurate 3D images. Additionally, they are used in astronomy to calculate the positions and movements of celestial objects.

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