Trigonometric function

Question

Suppose the terminal arm for the angle theta passes through the point (1,-4)

a). Draw the angle from the standard position and determine the length of the radius.

b). Find all 6 trigonometric ratios (3 primary and 3 reciprocal). Keep the numbers in EXACT form( e.g., if you get a radical such as square root 2, don’t change it to decimal.

Answer 1

(-1,-4) is in quadrant III (-1,-4) = (x,y) where x = rsin(theta) and y = rcos(theta) -1=rsin(theta) and -4=cos(theta) -4/-1 = 4 = tan(theta) (-1,-4) in polar coordinates = (4.1, 256) or (4.1, 1.4pi)

the reference angle = tan^-1(4) = about 76 degrees

in quadrant III that's 180+76 = 256 degrees

r= sqr(4^2 +1^2) = sqr17 = about 4.1 = radius

256 degrees = 256/180 pi radians = about 1.4 pi

tan(theta) = 4

cot(theta) = 1/4

sin(theta) = -4/sqr17

csc(theta) = -sqr17/4

cos(theta) = -1/sqr17

sec(thet) =-sqr17