How do you find the solution to csctheta-1=3csctheta-11 if 0<=theta<2pi?

2 Answers
Somebody N.
Nov 9, 2017

theta~~ 0.20136 , 2.9402 radians

Explanation:

csc(theta)-1=3csctheta-11

csctheta-3csctheta=-11=1

2csctheta=10=>csctheta=5

csctheta=1/sintheta

:.

1/sintheta=5

sintheta=1/5=> theta~~ 0.20136 , 2.9402 radians

Nghi N
Nov 10, 2017

11^@54; 168^@46

Explanation:

Transform equation in terms of sin t:
1/sin t - 1 = 3/sin t - 11
10 = 2/sin t
sin t = 2/10 = 1/5
Calculator and unit circle give:
t = 11^@54 and t = 180 - 11.54 = 168^@46

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