Please show complete work to answers.

QUIZ Discussion

Use the given information about  to find the exact values of

cos (/2)

cos () = 3/5 where 0 /2

Select a different trigonometric function from the list below. Find the amplitude, period, and phase shift for your trigonometric function and post a graph of at least one period.

y = cos (1/2 x + π/2) +3

solve the equation, giving the exact solutions which lie in [0, 2π]

sin(x) + cos(x) = 1

Start by drawing a diagram of the situation in your selected word problem. Clearly label which direction is north, south, east, and west in your diagram, and label the known sides and angles in your triangle. Then use the Law of Cosines or Law of Sines to solve the problem.

A vehicle travels due west for 30 miles. Then it turns and goes 30 miles in the direction of S68ᵒW. How far is it from the starting place?

Find 2 ordered pairs of numbers in the polar form (r,θ) which satisfy your equation. Then find the points in Cartesian coordinates (x,y) that are equivalent to the two polar points you just found.

Plug that angle in for θ in your equation, and compute the corresponding value of r.

x = rcosθ and y = rsinθ

Write your equivalent Cartesian coordinates points in form (x,y)

CHECK: Do your polar points and their corresponding Cartesian coordinates land on the same point when graphed?

r = 3cosθ

Write your answer in the polar coordinates form (r, θ)

Repeat the steps above for another chosen value of θ.

Use the conversion formulas for converting polar points to Cartesian coordinates.

Pick a set of vectors u and v from the list below, and do the following 5 items:

A. Draw each vector in standard position.

B. Find the magnitude of vector u: ||u||

C. Find the difference of vectors < u - v >

D. Find the magnitude of vector < u - v > : || u - v ||

E. Find the angle θ, in degrees, between the vectors u and v. θ should be between 0° and 180°

2. u = < 4, 5 > and v = < -1, -15 >

Determine if the given equation is a parabola, ellipse, circle, or hyperbola.

If it is a parabola find the vertex point, focus, directrix, and determine which way it will open (up, down, right, or left).

If it is an ellipse, find the center point and vertices, and determine if it is short and wide or tall and thin.

If it is a circle, find the center and radius.

If it is a hyperbola, find the center point and vertices, and determine which way it will open (up and down, or right and left).

(y+2)2 = 4(x+6)