Find the solutions of the equation 3cos(2 theta) - 5cos(theta) + 2 = 0 in the interval 0 < theta < 2pi.

3cos^2(theta) - 3sin^2(theta) - 5cos(theta) + 2 = 0

3cos^2(theta) + 3cos^2(theta) - 3 - 5cos(theta) + 2 = 0

6cos^2(theta) - 5cos(theta) - 1 = 0

delta = 25 + 24 = 49

cos(theta) = (5 - 7)/12 = -1/6 or cos(theta) = 1

theta = 0 or arccos(-1/6) or 2pi - arccos(-1/6) or 2pi

PW
Answered by Piotr W. Maths tutor

5024 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

I can differentiate exponentials (e^x), but how can I differentiate ln(x)?


Differentiate y = 3x4-8x3-3


A curve is defined by the parametric equations x = 3 - 4t, and y = 1 + 2/t. Find dy/dx in terms of t.


Solve 4cos(2x )+ 2sin(2x) = 1 given -90° < x < 90°. Write 4cos(2x )+ 2sin(2x) in the form Rcos(2x - a), where R and a are constants.


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences