Find, in radians, the general solution of the equation cos(3x) = 0.5giving your answer in terms of pi

we have   cos (3x) = 0.5  (1) we know that in the interval between [-pi; pi] there are two values that satify the equation cos(y) = 0.5  (2) the two solutions are y=pi/3 and y=-pi/3 in this interval.  More generally, there are two grop of solutions which are y=(pi/3) + 2kpi and y=(-pi/3) + 2kpi  (were k is a natural integer) From the equations (1) and (2) we can thus set : 3x = y  <=>  3x = (pi/3) + 2k    and    3x = (-pi/3) + 2k*pi so by dividing each part of the equation by 3 we get   x= (pi/9) + (2k/3)*pi  and x = (-pi/9) + (2k/3)*pi

MB
Answered by Marie B. Maths tutor

7013 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can you find the coefficients of a monic quadratic when you know only one non-real root?


given that at a time t, a particle is accelerating in the positive x-direction at 1/t ms^-2, calculate the velocity and the displacement of the particle at time t = 2s


The curve C has the parametric equations x=4t+3 and y+ 4t +8 +5/(2t). Find the value of dy/dx at the point on curve C where t=2.


When solving a trigonometric equation, like sin(x) = -1/3 for 0 ≤ x < 2π, why do I get an answer outside the range? Why are there many correct answers for the value of x?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning