Using double angles to find value of

[aeromat]

Homework Statement

Homework Equations

The Attempt at a Solution

I know the following:
sin^2x = 8/9
the hyp. is 9, the "y" value is 8.
Therefore, the "x" value has to be $$\sqrt{17}$$

What is the next step?

 

[Mark44]

You are given that x is in Quadrant II, so sin(x) >= 0 and cos(x) <= 0.
You are also given that sin²(x) = 8/9, so you can easily find cos²(x).

Now find sin(x) and cos(x) by taking the square root with the appropriate sign, and you can evaluate sin(2x) = 2sin(x)cos(x).

 

[aeromat]

Im sorry I should've really thought before I posted. I actually got through A,B, and C. However, d (with sin3(x)) is confusing me.

The double angle formula for it will be:
sin3x = sin0.5xcos0.5x correct?
But then, when I sub in known values, I don't receive the correct answer:

-10*root 2
--------------
27

 

[Mark44]

Im sorry I should've really thought before I posted. I actually got through A,B, and C. However, d (with sin3(x)) is confusing me.

The double angle formula for it will be:
sin3x = sin0.5xcos0.5x correct?

No - why would you think that. sin(3x) = sin(2x + x). Use the addition formula and then the double angle formula to get things in terms of sin(x) and cos(x), which you already know.

But then, when I sub in known values, I don't receive the correct answer:

-10*root 2
--------------
27

 

[aeromat]

I'm sorry but we just started this unit and I am not sure how I would do that:

Use the addition formula and then the double angle formula to get things in terms of sin(x) and cos(x), which you already know.

 

[Bohrok]

sin(3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x)

Then you use the double-angle formulas for sin(2x) and cos(2x).

 

[aeromat]

sin(3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x)

Then you use the double-angle formulas for sin(2x) and cos(2x).

I'm sorry but I have no idea how you would do that. Would you mind explaining to me step-by-step?

 

[MysticDude]

Well you have sin(2x)cos(x) + cos(2x)sin(x). In other words. Use the double angle formulas for the bold areas. Like the first part would be 2sin(x)cos(x)cos(x) or 2sin(x)cos²(x). The second part is to substitute one of the double angle formulas for cos(2x), look at the second version as I think that one will help a lot, and then substitute your x values for each. Hope I make sense! :D