# Thread: sin a sinx+ b cosx

1. ## sin a sinx+ b cosx

a)Express 2cosx+ sinx in the form Rcos(x-A)

b) Solve the equation 2cosx+ sinx= 1 giving all solutions between 0 and 360 degrees.

c) Find the exact range of values of the constant K for wich the equation 2cosx+sinx =K has real solutions for x

Id really appreciate it if somone helped me with this question.
I can do part a but not b and c

Thank you.

2. Originally Posted by Oasis1993
a)Express 2cosx+ sinx in the form Rcos(x-A)

b) Solve the equation 2cosx+ sinx= 1 giving all solutions between 0 and 360 degrees.

c) Find the exact range of values of the constant K for wich the equation 2cosx+sinx =K has real solutions for x

Id really appreciate it if somone helped me with this question.
I can do part a but not b and c

Thank you.
HI

(b) $\displaystyle \sqrt{5}\cos (x-26.57)=1$

$\displaystyle \cos (x-26.57)=\frac{1}{\sqrt{5}}$

x-26.57=63.43 , 296.57

Can you continue ?

(c) $\displaystyle \sqrt{5}\leq K\leq \sqrt{5}$

Graph $\displaystyle \sqrt{5}\cos (x-26.57)$ and you should be able to see .