For what angles theta B/T 0 & 360 does cos theta = -sin theta?
It's simple question, but I could not think of any angles that would make this statement true. Maybe I'm missing something...
Here's a hint -- there are two places between 0 and 360 degrees where cos(theta) = -sin(theta). Can you see that at 45 degrees cos(theta) = sin(theta)? For this angle you are in quadrant 1, where both sin and cos are positive. But what about other quadrants where sin and cos have opposiite signs? I trust this helps - now post back with what you think the answer is.
$\displaystyle Cos\theta$ in a unit circle gives the x co-ordinate of a point on the circumference.
$\displaystyle Sin\theta$ gives the y co-ordinate of the same point.
$\displaystyle -Sin\theta$ is the negative of the y co-ordinate.
To be equal numerically, the angles cut the quadrants in two equal parts,
hence the angles are 45, 135, 225 and 315 degrees.
For 2 of these, the x and y co-ordinates of the 4 points are equal numerically and have opposite sign.
In which quadrants are the co-ordinates of opposite sign?