Final Exam Math

3<cos 50o + sin 50o> + 9<cos50o + sin 50o>

12<cos 50o + sin 50o>

What is the period of y=sin(2x)

180 degrees

(5 - 2i) equation(8 + 3i)

34-31i/73

Convert (3 - 4i) to polar form.

5(cos 306.87 + i sin 306.87)

The following is a graphic representation of which vector expression? (5 lines)

<i + 6j> + <7i + 6j>

u = <3, -2>, v = <-5, 7>, w = <-4, 6> Find v + 2u.

First complete the multiplication of 2u: 2<3, -2> = <6, -4>. Then add v with 2u: <-5 + 6, 7 + (-4)> = <1, 3>

x^2/625 + y^2/400 = 1

center: (0,0); Vertices:(-25, 0),(25,0); Foci: (-15,0)

9x^2 + 2y^2 = 18

center: (0,0); Verticies: (-9,0)(9,0); Foci: (-√77,0), (√77,0)

Convert 9 (cos 100o + i sin 100o) to rectangular form.

(- 1.56 + 8.86i)

Which of the following could be represented by the point graphed on the complex plane? (3rd quadrant)

(- 4 - 10i)

(3 + 4i) + (- 7 - 8i)

(- 4 - 4i)

Convert 6(cos 180o + i sin 180o) to rectangular form.

(- 6 + 0i)

(12 + 2i) - (- 8 + 5i)

(20 - 3i)

(5 + 3i)(8 - 4i)

(52 + 4i)

convert 40 degrees to radians

2pi/9

12(cos 310o + i sin 310o) / 4(cos 100o + i sin 100o)

3(cos 210o + i sin 210o)

Which of the following is the graph of (3 - 2i)? (The horizontal axis and vertical axis are scaled with each tick mark reprenting one unit.) (This one is also a graph which quadrant is the dot in)

4th quadrant

A ranger spots a fire from a 73 foot tower in Yellowstone National Park. She measures the angle of depression to be 16 degrees. What expression would you use to find the distance to the fire?

74 cot 73

u = <3, -2>, v = <-5, 7>, w = <-4, 6> Find 3v - w.

<-11, 15>

<3i + 5j> - <6i - 2j>

<-3i + 7j>

x^2 + y^2 + 30x + 6y + 233 = 0

Center (-15, -3) Radius = 1

(x+5)^2 /25 + (y + 1)^2 /9 = 1

Center: (-5, -1); Vertices: (-10, -1), (0, -1); Foci: (-9, -1), (-1, -1)

Cosine function Amplitude : 1/2 Period: pi Phase shift: pi/2 Vertica shift: -1

Period to find k: 2pi/k = pi kpi = 2pi k = 2 Phase shift formula -c/k = pi/2 -c/2 = pi/2 -2c = 2pi c = -pi we know that h = -1 and amplitude is 1/2 y = Asin(kθ + c) + h y = 1/2sin(2θ -pi) -1

2(cos 50o + i sin 50o) 9(cos 150o + i sin 150o)

To multiply complex numbers in polar form, multiply the moduli and add the arguments. 2(9) = 18 50 + 150 = 200 18(cos 200o + i sin 200o)

y - 2sin(2θ+pi) - 3 y = Asin(kθ + c) + h The formula for period is 2pi/k in this function k = 2 period = 2pi/2

pi

find the exact value of sin^-1(√3/2)

pi/3

y = 1/2 * sinθ

small swiggly inbetween and under pi and 2pi and over inbetween 2pi and 3pi

y = 4sin2θ which graph represents it

swiggly graph that touches 4 on the y axis, and pi/2, pi, and 3pi/2 on the x axis

y = sin(θ - 5pi/6) Graph it

swiggly over pi, down through 2pi and over 3 pi

y = 2cos there

through 2 and under pi, over 2pi and under 3pi

(y - 3)^2/225 - (x-5)^2/400 = 1

vertices: (5,18),(5,-12); Foci: (5,28), (5,-22)

Match graph with equation Horizontal Circle

x^2/25 + y^2/9 = 1

match graph with equation. Vertical circle.

y^2/25 + x^2/9 = 1

Match graph with equation Downward Mountain and upward Mountain

y^2/9 - x^2/25 = 1

y = -2cos(1/2θ) + 4 identify amplitude

|-2| = 2

Given that u = < 2, -3 > and v = < 3, 1 >, which of these could be the sum shown in the graph?

- 2u + 3v

what is the exact value of csc 4pi/3

-2√3/3

Sin θ counter clockwise swirl -420

-√3/2

cos^-1(1)

0

what is the exact value of sin pi/6

1/2

Find the component form of a vector with a magnitude of 5 and a direction of 315 degrees.

5√2/2, - 5√2/2

Find the components of a vector with an initial point of (3, -2) and a terminal point (7, -4).

<7 - 3, -4 - (-2)> = <4, -2>

Write the equation of the sine function that has the given characteristics: y = Asin(kθ + c) + h amplitude: 3 Period: pi

Amplitude |A| = 3 A = 3 Period 2pi/k = pi kpi = 2pi k = 2 Now, substitute both of these back into the parent function: y = 3sin2θ

Write the equation of the sine function that has the given characteristics: Amplitude 1/3 Period: pi

Amplitude |A| = 3 A = 3 Period 2pi/k = pi kpi = 2pi k = 2 y = 1/3sin2θ

Cosine function Amplitude : 3 Period: pi/2 Phase shift: pi Vertica shift: -2

Period to find k: 2pi/k = pi/2 kpi = 4pi k = 4 Phase shift formula -c/k = pi -c/4 = pi -c = 4pi c = -4pi we know that h = -2 and amplitude is 3 y = Asin(kθ + c) + h y = 3sin(4θ + -4pi) -2

For vectors d and n, n = -3d. What is true about vectors n and d?

The magnitude of n is 3 times as large as d's magnitude and the directions are opposite.

sin^-1(cos(pi/3))

pi/3

Which of the following is the graph of equation? 3(cos60 + isin60)

pi/3 on the unit circle

sin^-1(cos(pi/4))

pi/4

Find the phase shift of the function: y = 3cos(2θ - pi/3) + 4

pi/6

Vertices at (±7, 0), foci at (±9, 0)

x^2/49 -y^2/32 = 1

match graph with equation. two boobs staring at each other

x^2/9 - y^2/25 = 1

y = -3sin(2θ) identify the aplitude

|-3| = 3

sin x = 9/10 Find cos x

√19/10

Cos θ Counterclockwise Swirl -405

√2/2

Find the modulus and conjugate of (4 - 7i).

√65, (4 + 7i)

Find the exact value of the magnitude of the following vector: <6, -2, 7>

√89

Find the modulus of (5 + 8i)

√89