SOLUTION: Can you help me to solve the following question: The vertical displacement of the end of a robot arm (in mm) at time t (in seconds) is given by y=1+4cos(2t)-4sin(4t) a) fi

Question 869777: Can you help me to solve the following question:
The vertical displacement of the end of a robot arm (in mm) at time t (in seconds) is given by
y=1+4cos(2t)-4sin(4t)
a) find all times, t>0 (in exact form i.e. in terms of pi) where the vertical displacement is 1mm, i.e. y=1
b) what is the first time, t>0 that the vertical displacement is 1mm? give you answer exactly and to 2 decimal places?

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let x = 2t
Then we can write the expression as
y = 1 + 4cos(x) - 4sin(2x)
y = 1 implies 4cos(x) - 4sin(2x) = 0
Divide through by 4 and replace sin(2x) with 2sin(x)cos(x):
cos(x) - 2sin(x)cos(x) = 0
Factor:
cos(x)(1 - 2sin(x)) = 0
This gives cos(x) = 0, or sin(x) = 1/2
I'll let you take it from here (don't forget x=2t)
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