Convert the angle 13 pi9 to degrees Find one negative angle

Convert the angle 13 pi/9 to degrees Find one negative angle that is coterminal with 7 pi/4 Find the exact values of the six trigonometric ratios of the angle theta in the triangle. Then find the angle theta. Round to one decimal place.

Solution

1 a) 13pi/9 to degrees

pi rad --- 180 deg

So, 1 rad -- (180/pi)

13pi/9 rad --- (180/pi)*13pi/9 = 180*13/9 =260 deg

b) coterminal angle for 7pi/4 = pi +3pi/4

2pi - 7pi/4 = - pi/4 ( -ve coterminal angle)

c) sintheta = height/hypo = 24/25

csctheta = 1/sinthea = 25/24

costheta = 7/25

sectheta = 1/costheta = 25/7

tantheta = 24/7

cot theta = 1/tantheta = 7/24

theta = sin^-1(24/25) = 73.74 deg