IF
$$4\sin+4\cos=0$$
THEN FIND OTHER TRIGONOMETRIC RATIOS.

Question

IF
$$4\sin+4\cos=0$$
THEN FIND OTHER TRIGONOMETRIC RATIOS.

directrix · Answer

This angle could be in Quadrant 2 or in Quadrant 4. Look at the instructions and post which one. Thanks. @Rohan28

anonymous · Answer

the problem given is only this much no other detail

debbieg · Answer

First of all, there is no such thing as: $4\sin+4\cos$. That is mathematical gobbletygook. :) A function has to have an input, so to say "sin" without an input is like saying $\Large \sqrt{~~}$ .

So what you mean is:

$4\sin x+4\cos x=0$

which means that:

$4\sin x=-4\cos x$
$\sin x=-\cos x$

This can be true only when the sine and cosine functions have different signs (Q2 or Q4) and when they are equal in absolute value, which happens only when the reference angle is $\pi/4$. So there is an angle in Q2 and another in Q4 where the equation is satisfied, as @Directrix pointed out. Do you see what those 2 angles are?

Thus, without more information, you can only come up with the other trig functions to within a $\pm$ value (except for cotangent, that one you can determine exactly, because it has the same sign in Q2 as it does in Q4).