From the information given, find the quadrant in which the terminal point determined by t lies. sin(t) < 0 and cos(t) < 0

Question

a. I

b. II

c. III

d. IV

Answer 1

From the information given, find the quadrant in which the terminal point determined by t lies. sin(t) < 0 and cos(t) < 0

I use the mnemonic ASTC or All Students Take Calculus to remember the signs of the trig functions in counterclockwise order as I go from Quadrants I to Quadrant IV.

Recall Quadrant I is where x and y>0, Quadrant II is where x<0 and y>0, Quadrant III is where x<0 and y<0, and Quadrant IV where x>0 and y<0.

All: In Quadrant I, All trig functions are positive. The sine, cosine, tangent and all three of their reciprocals are positive.

Students: In Quadrant II, the Sine and its reciprocal (cosecant) are positive. The rest are negative.

Take: In Quadrant III, the Tangent and its reciprocal (cotangent) are positive. The rest are negative.

Calculus: In Quadrant IV, the Cosine and its reciprocal (secant) are positive. The rest are negative.

So when sin(t) and cos(t) are both negative, t must be in Quadrant III where 180^o < t < 270^o