"After showing that #2sectheta-tantheta=3# can be written as #sqrt10cos(theta-18.4)=2#, solve for #theta# (#0<theta<360#)". I proved the first part, can somebody please solve for #theta#?
1 Answer
Oct 13, 2015
Solve 2sec x - tan x = 3
Ans:
Explanation:
I solve it another way.
2 - sin x = 3cos x
sin x + 3cos x = 2.(1)
Call
Equation (1) -->
sinx.cos a + sin a.cos x = 2cos a = 0.632
sin (x + a) = sin (x + 71.57) = 0.632. Two solutions:
a. (x + 71.57) = 39.20 --> x = 39.20 - 71.57 = - 32.37 (or
b. x + 71.57 = 180 - 39.20 = 140.80.
x = 140.80 - 71.57 =
Check by calculator.
x = 69.23 --> 2sec = 5.64 --> tan x = 2.64.
2sec - tan x = 5.64 - 2.64 = 3. OK
x = - 32.37 --> 2sec = 2.37 --> tan x = - 0.63
2sec - tan x = 2.37 + 0.63 = 3. OK