# Math Help - Another trigonometric equation

1. ## Another trigonometric equation

If I had the equation 2cosx + sinx = 1 then I could express it as
√5 cos (x-26.6) = 1. I have no problem when it's like this

However, if it was 2sinx + cosx = 1, how could I do it? would it be
√5 sin (x - 63.4) = 1?

If I go further to find the values of x here, I calculate
sin^(-1) of 1/√5 which is 26.6, and then for x I get 90 and 396.8, but because it's not under 360 I take that value away and get 36.8.

So, I said x was 36.8 and 90. Whenever I put these back into the equation though, it doesn't result in 1, it results in two. Does anyone know why this is and can point out where I'm going wrong?
Thanks if you can help

2. Originally Posted by db5vry
If I had the equation 2cosx + sinx = 1 then I could express it as
√5 cos (x-26.6) = 1. I have no problem when it's like this

However, if it was 2sinx + cosx = 1, how could I do it? would it be
√5 sin (x - 63.4) = 1?

If I go further to find the values of x here, I calculate
sin^(-1) of 1/√5 which is 26.6, and then for x I get 90 and 396.8, but because it's not under 360 I take that value away and get 36.8.

So, I said x was 36.8 and 90. Whenever I put these back into the equation though, it doesn't result in 1, it results in two. Does anyone know why this is and can point out where I'm going wrong?
Thanks if you can help
sinA*cosB + cosA*sinB = sin(A+B)

3. Originally Posted by db5vry
However, if it was 2sinx + cosx = 1, how could I do it? would it be
√5 sin (x - 63.4) = 1?
$2\sin x+ \cos x =1$

Let $2 = r \cos y$ and $1=r \sin y$

$r^2 = \sqrt{2^2+1^2}=\sqrt{5}$

$\tan y = \frac{1}{2} \Rightarrow y = 26.6^{\circ}$

so it becomes,

$r[\sin x \cos y+\cos x \sin y]=1$

$\sin (x+y)=\frac{1}{r}$

$\sin (x+26.6)=\frac{1}{\sqrt 5}$

Originally Posted by db5vry
If I go further to find the values of x here, I calculate
sin^(-1) of 1/√5 which is 26.6, and then for x I get 90 and 396.8 (HOW?)(It should be 386.6), but because it's not under 360 I take that value away and get 36.8 (HOW?).
Did you get your mistake now??