Question

1. How could you use the unit circle to determine the tangent of
a given angle measure? Explain.

2. Explain why x-coordinates of points on the unit circle are the same as cosine of the associated angle measure.

Answer #1

On a circle, why is cos(θ)=xrcos(θ)=xr equivalent to
cos(θ)=adjacenthypotenusecos(θ)=adjacenthypotenuse ?
On a unit circle, is the x-coordinate the same ascos(θ)cos(θ)
and why is the y-coordinate the same as sin(θ)sin(θ) ?
Explain how to how to evaluate sin(300∘)sin(300∘) using a
reference triangle. Your explanation should include a drawing that
shows...
The unit circle
The angle in standard form
The reference angle and reference triangle
The coordinates of the point
Draw a unit circle from scratch (just like in the video above)....

How could one measure the Brewster's angle only given laser,
glass, protractor and a polarizer? That is, what independent
experiment could one do to measure the Brewster angle? No great
detail needed

Explain how a drone that is flown high above a city could be
used calculate the height of a building or other landmark, using a
method like the one you used to find the height of the Bell Tower.
Give detailed step by step instructions that a classmate could
follow. Include a figure.
I listed the steps below:
Steps to calculating the height of a building using a drone:
1. Use the drone’s ability to measure
X and Y coordinates...

1) find the endpoint of the radius of the radius of
the unit circle that makes 1680 degree angle with the positive
horizontal axis.
2) what is the slope of the radius of the unit of the circle that
has a 600 degree angle with positive horizontal axis.
3) value of cos15pie/4 and sin15pie/4
4) find all numbers x that satisfy the equation:
ln(x+8)+ln(x+4)=3

Please solve all if possible
1. a) Find an equation of the tangent line to the graph of
y=x(x+1)^6 at the point where x=−2.
b) [2 points] State the coordinates of the x-intercept of the
line.
2. Find f(x) by solving the initial value
problem.
f′(x)=2−3x^ −2, f(3)=5.
3. Determine the intervals where the function f(x)=2x^2−1/4x^4
is increasing and decreasing, and also both coordinates of all
local extrema, if any. Label each extremum as a maximum or a
minimum.

Q-1
please uplode a clear photo
- determine the unit tangent and normal vector to the curve
r(t)=< 2t^2 , 4t > , at t=1

Consider the surface z=3x^2*y+y^3-3x^2-3y^2+2
a. A boy is playing frisbee on this surface standing at
(-1,0,-1). If he walks in the direction <4,-3> is he going
uphill or downhill? How steep is the surface in that direction?
Explain
b. Find the cosine of the angle of inclination of the tangent
plane at the point (1,2,1)
c. At which 4 points is the angle of inclination of the tangent
plane equal to 0?

1.A circular arc of length 10 cm subtends the central angle
θ on a circle with radius 6 cm.
(a) Find the degree measure of the central angle θ. Give
your answer correct to 2 decimal places.
θ = °
(b) Find the area of the sector determined by θ. Give your
answer correct to 2 decimal places.
Area = cm2
2.The 660°angle is in standard position. Determine which of the
choices are coterminal angles. (Select all that apply)660°
570°, 1380°, 300°,...

What method could you use to determine the volume of a sphere,
or of any object? Explain how Archimedes could have determined if
his kings crown is indeed made of pure gold while taking a bath at
the same time?

consider the function f(x)=-x2+90x-30
1)determine f'(x) (use lim method)
2)determine the equation of the line tangent to f(x) at
x=1

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