1. ## More Trig

Hi,

I'm lost on how to do part b) of the following question:

can anyone help?

Explanation is needed! =) Thanks

2. First thing I would do is take the sine of both sides, and use the addition of angles formula on the RHS.

3. Originally Posted by Ackbeet
First thing I would do is take the sine of both sides, and use the addition of angles formula on the RHS.
Ok, so I've got:

sin (arcsin(1-2x)) = sin(pi/3) - sin(arcsin(x))
using the triangle rule from yesterday
it simplifies to: 1-2x = 0.5 - x
so x = 0.5

but the restriction requires x to be less than 0.5?

4. The RHS does not simplify as you have indicated. You have to use the addition of angles formula.

[EDIT] Also, don't forget the Commandments of Algebra.

5. Originally Posted by Ackbeet
The RHS does not simplify as you have indicated. You have to use the addition of angles formula.

[EDIT] Also, don't forget the Commandments of Algebra.
oh yeah sorry.

So its:

1-2x = sin(pi/3)cos(arcsinx) - cos(pi/3)sin(arcsinx)
1-2x = √3/2.(√(1-x^2)) - 0.5x

then i get:

12x^2 -12x +1 = 0

is it right up to there? then i can just use x= -b +/- .....

6. Yeah, you skipped a few steps, but I would agree with your conclusion. You do need to be careful: in squaring the equation to end up with your quadratic, you may have introduced spurious solutions. So you should definitely double-check against your allowed x's. Good work!

7. Thanks! I've gotten through this one now =)

Soon I'll have a few more worries! ^^

8. You're welcome! Have a good one.