Solve for sin x: 5sec^2x + 3tan^2x = 9 using trig identities

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In summary, the conversation discusses solving for the value of sinx given the equation 5sec^2+3tan^2 = 9 and using trigonometric identities to find the solution. The conversation also mentions finding two possible values for x and using the relationship between tanx and sinx to find the values for sinx.
  • #1
ibysaiyan
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Homework Statement


Given that 5sec^2+3tan^2 = 9
find sinx value

Homework Equations


trig. identities


The Attempt at a Solution


i started off by subbing. in sec2= 1+tan^2
=>
5(1+tan^2)+3tan^2= 9
5+8tan^2x = 9
8tan^2 = 4
tan^2 = 1/2 <--- no idea of this bit, as i am supposed to find sin x value =/ , hmm i even wonder if this right.
 
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  • #2
Yes it is correct. Take the square root and find the angles for the two values.
 
  • #3
tanx= [tex]\sqrt{}1/2[/tex]
x= inverse. sin [tex]\sqrt{}1/2[/tex] is that how i get values for sin?
 
  • #4
ibysaiyan said:
tanx= [tex]\sqrt{}1/2[/tex]
x= inverse. sin [tex]\sqrt{}1/2[/tex] is that how i get values for sin?

You will have two values, x2=a ⇒ x=±√a

Also if tanx=y, then x=tan-1(y). Where did you get inverse sine from?
 
  • #5
rock.freak667 said:
You will have two values, x2=a ⇒ x=±√a

Also if tanx=y, then x=tan-1(y). Where did you get inverse sine from?

Exactly lol that's what i thought.. the question wants me to get sinx values if possible :9.
 
  • #6
ibysaiyan said:
Exactly lol that's what i thought.. the question wants me to get sinx values if possible :9.

Sorry, I mis-read the question. While you can just find the values for x, and then find sinx.

You can also use tanx=sinx/cosx and then use cos2x=1-sin2x and solve for sinx.
 
  • #7
ah k, thanks for helping me out :).
 

1. What is the first step in solving this equation?

The first step in solving this equation is to rewrite the secant and tangent functions in terms of sine and cosine using the identity sec^2x = 1/cos^2x and tan^2x = sin^2x/cos^2x.

2. How do I simplify the equation after rewriting it?

After rewriting the equation, use the Pythagorean identity sin^2x + cos^2x = 1 to combine like terms and simplify the equation to a form of sin x = a, where a is a constant.

3. Can I solve for x using just the inverse sine function?

No, since the equation contains both sine and cosine functions, you will need to use the inverse tangent function to solve for x.

4. What do I do if the equation has multiple solutions?

If the equation has multiple solutions, you will need to use the general solution of inverse tangent to find all possible values of x.

5. Can I use a calculator to solve for x?

Yes, you can use a calculator to find the inverse tangent of the constant value to solve for x. Make sure your calculator is in the correct mode (degrees or radians) before calculating.

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