# All sin cos tan rule

The abbreviation for 'all sin cos tan' rule in trigonometry is ASTC. It can be memorized as "All Students Take Calculus". The first letter of the first word in this phrase is 'A'. This may be taken to indicate that all trigonometric ratios in the first quadrant are positive. The first letter of the second word Sindicates that sine and its reciprocal are positive in the 2nd quadrant. The first letter of the third word T indicates that tangent and its reciprocal is positive in the third quadrant. The first letter of the last word C indicates that cosine and its reciprocal are positive in the fourth quadrant.

## All sin cos tan rule:

1) When $\Theta$ lies in the first quadrant then all trigonometric ratios are positive.
2) When $\Theta$ lies in the second quadrant then sine and cosecant are positive other trigonometric ratios sin ,cosec, tan and cot are negative.
3) When $\Theta$ lies in the third quadrant then tangent and cotangent are positive other trigonometric ratios sin ,cosec, tan and cot are negative.
4) When $\Theta$ lies in the fourth quadrant then cosine and secant are positive other trigonometric ratios sin ,cosec, tan and cot are negative.