A calzone is divided into 24 equal pieces. Glenn and Ben each ate one eighth of the calzone on Thursday. The next day, Ben ate
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Answer:
For a point defined bt a radius R, and an angle θ measured from the positive x-axis (like the one in the image)
The transformation to rectangular coordinates is written as:
x = R*cos(θ)
y = R*sin(θ)
Here we are in the unit circle, so we have a radius equal to 1, so R = 1.
Then the exact coordinates of the point are:
(cos(θ), sin(θ))
2) We want to mark a point Q in the unit circle sch that the tangent has a value of 0.
Remember that:
tan(x) = sin(x)/cos(x)
So if sin(x) = 0, then:
tan(x) = sin(x)/cos(x) = 0/cos(x) = 0
So tan(x) is 0 in the points such that the sine function is zero.
These values are:
sin(0°) = 0
sin(180°) = 0
Then the two possible points where the tangent is zero are the ones drawn in the image below.
Answer:
a.
b.
Step-by-step explanation:
Remember that for any curve
The tangent vector is given by
And the normal vector is given by
a.
For this case, using the chain rule
And also remember that
Therefore
Similarly, using the quotient rule and the chain rule
And also
Therefore
Notice that
1.
2.
b.
Simlarly
and
Therefore
Then
and also
And since