SOLUTION: I have a similar question to one that has been answered. The vertical displacement of the end of a robot arm (in cm) at time t (in seconds) is given by y = 8+7cos3t + 7cos6t 1.

Question 966917: I have a similar question to one that has been answered.
The vertical displacement of the end of a robot arm (in cm) at time t (in seconds) is given by y = 8+7cos3t + 7cos6t
1. Find all times, t>0 (fractions of pi) where the vertical displacement is 8cm.
2. What is the first time t>0 that the vertical diplacement is 8cm?
This is what I have started doing:
Let x = 3t
y = 8 + 7cos(x) + 7cos(2x)
now do I divide out 7 (from cos(x) and cos(2x)) and use a trigonometric Identity cos(2x)? which gives me cos(x) + 2cos^2x-1
Any help in the right direction would be appreciated. Thankyou
Chad.
Answer by Murthy(22) (Show Source): You can put this solution on YOUR website!
Given, y = 8+7cos3t + 7cos6t
when y=8 cm
8=8+7cos3t + 7cos6t
can be rearranged as
7(cos3t+cos6t)=0
or cos3t+cos6t =0
2cos(9t/2).cos (3t/2)=0 {cosA + cosB = 2 cos(A+B/2).cos(A-B/2)}
or cos(9t/2).cos (3t/2)=0
This means either cos(9t/2)=0 or cos (3t/2)=0
if cos(9t/2)=0
9t/2= n(pi)/2
t=n(pi)/9
if cos (3t/2)=0
3t/2= n(pi)/2
t=n(pi)/3
The first time when displacement is 8 cm is t=pi/9
RELATED QUESTIONS
Can you help me to solve the following question: The vertical displacement of the end... (answered by htmentor)

I read through Question 869777, but did not understand the response given to it, is there (answered by KMST)

Hi, I would just like to say thank you for your help in advanced. My question is... (answered by Theo)

Suppose a robot has a straight arm 18 inches long, that can rotate about the origin in a... (answered by stanbon)

Hey guys , i need help with this question....i am totally stuck. the question is related... (answered by Fombitz)

URGENT Hello, I have an urgent problem to be solved... I thank in advance to whoever... (answered by ikleyn)

Points on the terminal sides of angles play an important part in the design of arms for... (answered by stanbon)

Rainbow Robots Inc. was putting on a big demomstration. Everyone came to watch the... (answered by mananth,MathTherapy,greenestamps,math_tutor2020)