Evaluate the following. Please sketch the angle, and state which quadrant it lands in. You can use your unit circle to answer these.

Question

Evaluate the following. Please sketch the angle, and state which quadrant it lands in. You can use your unit circle to answer these.

cos(− π/6)

sin (4π /3)

sec(−3π)

tan (−15π/4)

csc (− 5π /3)

cot (5π/6)

Answer 1

cos(-pi/6) = cos(-30 degrees) =cos30 = sqr3/2= about 1.732/2= .866

line from the origin, below the x axis in Quadrant 4

y = -x/sqr3 with x>0

sin(4pi/3) = sin(420 degrees) =sin60 = sqr3/2 = about 1.732/2= .866

a line from the origin, above the x axis in Quadrant 1

y=xsqr3, x>0

sec(-3pi) =sec(-pi)= sec(-180) = sec180 = 1/cos180 = 1/-1 =-1

negative x axis forms a -180 or 180 degree angle with the positive x axis

y=0, x<0

on the borderline between quadrants 2 and 3

tan(-15pi/4) = tan(pi/4)=tan45 = sqr2/2 = about 1.414/2= .707

l x=y, x>0, diagonal through the origin in quadrant 1

csc(-5pi/3)= csc(pi/3) = csc60 = 1/sin60 = 1/sqr3/2 = 2/sqr3 = 2sqr3/3 = about 2/3 times 1.732 = about 1.155

line in quadrant 1, from the origin, making a 60 degree angle with the positive x axis

y=xsqr3, x>0

cot(5pi/6) = cot150 = sqr3 = about 1.732

y=-x/sqr3, x<0, in quadrant 2