March 2, 2015

Homework Help: math (final trig problem)

Posted by jacob on Monday, April 30, 2007 at 10:33pm.

Solve for x on the interval [0,π/2):

cos^3(2x) + 3cos^2(2x) + 3cos(2x) = 4

I havent done trig for a while so what exactly does that mean in solving for x on that interval and how would i go about doing that?

Where are you getting these tough trig questions??

how about letting cos 2x = t
then your equation becomes
t^3 + 3t^2 + 3t - 4 = 0

using Newton's Method I was able to come up with ONE real root , t=.709976

so cos 2x = .709976
for 2x= .7813322 radians
and finally by dividing by 2
x = appr. .39

You can factorize the cubic equation Reiny gave above:

t^3 + 3t^2 + 3t - 4 = 0 --->

(t+1)^3 = 5 --->

t = -1 + 5^(1/3)

Count, now that was clever.
good for you to recognize the sequence
1,3,3,(1) in Pascal's triangle.

Answer this Question

First Name:
School Subject:

Related Questions

Trig - prove the identity (sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2 sinX^6= ...
math (trig) - i have some problems doing trig the first one is: Show that cos(x/...
Trig - Solve the trig equation exactly over the indicated interval. tanθ = ...
Math - Trig Substitution - How can I solve the integral of x^3√(9-x^2) dx ...
trig - I need help with finding the amplitude, period, and the interval. y=4-...
Math - Directions: Find the Location on Unit Circle, Period & General Solution ...
Trig Help! - Question: Trying to find cos π/12, if cos π/6 = square ...
trig - What kind of reflections are the following trig functions? y = 3cos(x-1) ...
Calculus - Use a trig identity to combine two functions into one so you can ...
Maths - Solve this equation fo rx in the interval 0<=x<=360 3sinxtanx=8 I ...