From Singapore. so it will be best to get taught by singapore style. Thank you so much

Question

The values of two of the trigonometric functions of θ are given. Find the values of the other trigonometric functions.

(a) sin 0.975, cos 0.222

(b) csc 4.872, cos 0.979

Answer 1

sinx = .975

cosx =.222

x = 77.173 degrees

the angle has to be in the 1st quadrant, as that's the only quadrant where both sines and cosines >0. that means the other 4 trig functions will also be >0

cscx = 1/sinx = 1/.975 = 1.026

secx = 1/cosx = 1/.222 = 4.505

tanx = sinx/cosx = .975/.222 = 4.392

cotx = cosx/sinx = .222/.975 = .228

cscx =4.872

cosx =.979

x = about 11.763 degrees

the angle is in the 1st quadrant, the only quadrant where both cosines and cosecants are both >0. That means all the other 4 trig functions will be >0

sinx= 1/cscx = 1/4.872 = about 0.205

secx = 1/cosx = 1/.979 = about 1.021

tanx = sinx/cosx = (1/4.872)/(1/.979) = .979/4.872 = .201

cotx = 1/tanx = 4.872/.979 = .977