Math Help - Solutions for sin and cos equations

1. Solutions for sin and cos equations

Really need help with how to figure these out.

Thanks
James

2. Re: Solutions for sin and cos equations

For the first one, rewrite the equation using the double-angle identity for sine, to get:

$2\sin(x)\cos(x)=\sqrt{2}\cos(x)$

Now, divide through by $\sqrt{2}$ then subtract $\cos(x)$ from both sides, factor and use the zero-factor property to equate both factors to zero and solve.

For the second one, use a Pythagorean identity to get a quadratic in $\sin(x)$ :

$2(1-\sin^2(x))+3\sin(x)=3$

Now, distribute, and arrange in standard quadratic form, and you will find it factors nicely, and use the zero-factor property to equate both factors to zero and solve.

3. Re: Solutions for sin and cos equations

James this is very easy

for the first remember that sin(2x) =2sinxcosx
therefore 2sinxcosx=sqrt(2)cosx
transfer to the frst term and factorize to find
cosx =0 and sinx=sqrt(2)/2 solve them .....

for the second substitute cos^2(x) =1-sin^2(x) and solve the quadratic equation that you will obtain for sinx ..it is easy

4. Re: Solutions for sin and cos equations

omg, thank you so much Mark and Mino!!!