Trig Problem- solve equation. Check

[FlopperJr]

Homework Statement

Solve the equation 5sin²x-3=0, given values of x in the interval -180≤x≤180 correct to 1 decimal place.

Homework Equations

for sin: take inverse
180-θ
±360

The Attempt at a Solution

I rearranged the equation to
sin²=3/5
but I am not quite sure what to do since sine is squared. I think it won't affect answer.

Then I did the inverse which was 36.9
subtrated 180 from inverse; 180- 36.9 = 143.1
Then I did 360±36.9 and 360±143.1
where both of these didn't fit in the interval.

Is this correct: x=36.9° and 143.1°

 

[SammyS]

Homework Statement

Solve the equation 5sin²x-3=0, given values of x in the interval -180≤x≤180 correct to 1 decimal place.

Homework Equations

for sin: take inverse
180-θ
±360

The Attempt at a Solution

I rearranged the equation to
sin²=3/5
but I'm not quite sure what to do since sine is squared. I think it won't affect answer.

Then I did the inverse which was 36.9
subtracted 180 from inverse; 180- 36.9 = 143.1
Then I did 360±36.9 and 360±143.1
where both of these didn't fit in the interval.

Is this correct: x=36.9° and 143.1°

What do you mean by " ... I'm not quite sure what to do since sine is squared. I think it won't affect answer." ?

Is the solution to u = 5/3 the same as the solution to u² = 5/3 ? ... Of course not.

 

[FlopperJr]

Aww. Alright. Then how would I do it if sin is squared? Sin^2=3/5

 

[SammyS]

Aww. Alright. Then how would I do it if sin is squared? Sin^2=3/5

That should be sin²(x) = 3/5.

Take the square root of both sides of the above equation just like you would to solve u² = 3/5 .

Don't forget the ± .

After that use the arc-sine function, sin^-1 .

Alternatively, you can use the identity, cos(2x) = 1 - 2sin²(x).

 

[FlopperJr]

Ohhh. So it would be sinx= +/- the sqr root 3/5. Which then the inverse would be 50.8. Then 180 minus 50.8 is 129.2. After that I would take those two answers and +/- 360 which doesn't work. So my two answers I got are 50.8 and 129.2.

 

[SammyS]

Ohhh. So it would be sinx= +/- the sqr root 3/5. Which then the inverse would be 50.8. Then 180 minus 50.8 is 129.2. After that I would take those two answers and +/- 360 which doesn't work. So my two answers I got are 50.8 and 129.2.

Those two answers are fine. They're for $\displaystyle \sin(x)=\sqrt{\frac{3}{5}}\,.$

Now find the solution for the ' - ' sign: $\displaystyle \sin(x)=-\sqrt{\frac{3}{5}}\,.$

 

[FlopperJr]

Okay, for negative square root:
The inverse is -50.8
180-(-50.8). Is 230.8 which doesn't fit the range
But if I subtract from 360 I get -129.2
So my my two answers for this is -50.8 and -129.2 giving me a total of four answers