Signs by Quadrant

The quadrant decides the signs. cos θ is the across, so it is positive right of the y-axis (quadrants I and IV). sin θ is the height, positive above the x-axis (I and II). Tangent is sine over cosine, $\tan\left(\theta\right) = \frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$, so it is positive where the two agree: quadrants I and III.

In quadrant II the point is left and up: cos −, sin +, so tan −. One mnemonic, of several, for which function is positive where: All Students Take Calculus, counterclockwise from quadrant I. All three are positive in I, only Sine in II, only Tangent in III, only Cosine in IV.