Determine the sign (+ or -) of each expression WITHOUT using a calculator.
The first quadrant of the graph gets A, the scecond one gets S, the third T, and the fourth C
The A means All functions
S is sine
T is tangent
C is cosine
if the angle is in the first/A quadrant all funcions (tan,sin,cos) will be positive
in the scecond/S quadrant any Sin function will be positive
in the third/T quadrant any Tan function will be positive
in the fourth/C quadrant any Cos function will be positive
A good way to remember ASTC would be All Star Trig Class with the first letter of each word being the Letters you need. Yeah it is kind of cheesey but it works.
Cos(143) would be negative because 143 degrees are in the scecond/S quadrant which only has Sin funtions being positive and we are using a Cos function.
Sin(7pi/8): 7pi/8 is 157.5 degrees which is in the Scecond/S quadrant we are using a Sin function so it is positive.
Tan(192) is positive because 192 degrees would be in the/T third quadrant which has Tan functions positive.
Sec(-4pi/5) is 1/cos of -144 degrees. if we go back from 0 degrees by 144 degrees we get 216 degrees which is in the third/T quadrant. We are using a Sin function not a Tan funcion so it would be negative.
Hope that helps!