Posted by Anonymous on Tuesday, May 22, 2012 at 11:27pm.
Find all solutions of cos 2x + √2/2 =0.
a) + or  3/8pi +Kpi
b) 2/3pi + Kpi, 5/3pi + Kpi
c) + or  2/5 +Kpi
d) 2/3 pi + 2Kpi, 5/3pi + 2Kpi
I really need help on this question :(

trig  Reiny, Wednesday, May 23, 2012 at 4:56am
cos 2x + √2/2 =0
cos 2x = √2/2
I know cos π/4 = √2/2 or cos 45° = +√2/2
but 2x could be in II or III
2x = ππ/4 or 2x = π + π/4
2x = 3π/4 or 2x = 5π/4
x = 3π/8 or x = 5π/8 > 67.5° or 112.5°
but the period of cos 2x = π
so adding/subtraction multiples of π to an answer will yield more answers
general solution
x = 3π/8 + kπ, x = 5π/8 + kπ
a) fits the first of my solutions, but does not include the 2nd part of the solution
the others are not correct.
BTW, you can illustrate my 2nd solution, which they don't have, on a calculator
e.g. let x = 112.5° + 17(180)° = 3172.5
LS = cos 2(3172.5) + √2/2
= .707106781 + .707106781
= 0
= RS
Answer This Question
Related Questions
 trig  Solve cos x1 = sin^2 x Find all solutions on the interval [0,2pi) a. x=...
 precalc  Can someone help me find the exact value of 4csc(3pi/4)cot(pi/4)? ...
 CALCULUS  What is the following limit? lim as n goes to infinity of (pi/n) (sin...
 CALCULUS LIMITS  What is the following limit? lim as n goes to infinity of (pi/...
 Calculus  What is the following limit? lim as n goes to infinity of (pi/n) (sin...
 PreCalculuscheck answers  State the period and phase shift of the function y...
 Calculus  Determine whether the curve has a tangent at the indicated point. f(x...
 trig  Solve the equation for cos thetatan theta=0 for greater than or egual to...
 Math  Test for symmetry with repsect to Q=pi/2, the polar axis, and the pole. ...
 Math  Test for symmetry with repsect to Q=pi/2, the polar axis, and the pole. r...
More Related Questions