# Thread: Simultaneous equation with cos or sin

1. ## Simultaneous equation with cos or sin

Find P and Q

$
Pcos20-Qcos50=16cos45
$

$
Psin20+Qsin50=16sin45

$

what i did was find P which =

$

(16cos45+Qcos50)/cos20

$

then sub that in the first equation.

so it would be $[16cos45+Qcos50-Qcos50=16cos45]$

but that's not going to find Q

Any help is appreciated!

2. Originally Posted by BabyMilo
Find P and Q

$
Pcos20-Qcos50=16cos45
$

$
Psin20+Qsin50=16sin45

$

what i did was find P which =

$

(16cos45+Qcos50)/cos20

$

then sub that in the first equation.

try substituting it into the 2nd equation instead
...

3. lol i realise that but still cant do it really!

4. Originally Posted by BabyMilo
lol i realise that but still cant do it really!
why not?

$\frac{16\cos(45)+Q\cos(50)}{\cos(20)} \cdot \sin(20) + Q\sin(50) = 16\sin(45)
$

multiply by $\cos(20)$ to clear the fraction ...

$[16\cos(45)+Q\cos(50)] \sin(20) + Q\sin(50)\cos(20) = 16\sin(45)\cos(20)$

finish up by isolating $Q$

5. thanks! although worked it out before your post!
thanks though! hehe!