trianglestriangles 100 50 25 10 5graphsgraphs polar form functionsfunctions leftoversleftovers...

TrianglesTrianglesTrianglesTriangles

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GraphsGraphsGraphsGraphs Polar FormPolar FormPolar FormPolar Form FunctionsFunctionsFunctionsFunctions LeftoversLeftoversLeftoversLeftovers

Review for the FinalReview for the Final

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The 104 ChallengeThe 104 ChallengeReview for the FinalReview for the Final

Final Round

Triangles

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In any right triangle, the sum of In any right triangle, the sum of the squares of the sides is equal the squares of the sides is equal

to the square of the to the square of the hypotenuse.hypotenuse.

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5 Point Question5 Point Question

What is the Pythagorean Theorem?What is the Pythagorean Theorem?

In the triangle ABC, C = 90In the triangle ABC, C = 90oo, A = 25, A = 25oo and a = 3. Find b.and a = 3. Find b.

10 Point Question10 Point Question

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b = 6.433b = 6.433

11.4911.49

25 Point Question25 Point Question

Find c in the triangle below:Find c in the triangle below:

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12 12 cmcm cc

3838oo

102102oo

13.099 13.099 cmcm

50 Point Question50 Point Question

Find the length of the missing side in Find the length of the missing side in the triangle below. the triangle below.

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6868oo

13 cm13 cm

10 cm10 cm

Find all three missing angles in the Find all three missing angles in the triangle below.triangle below.

100 Point Question100 Point Question

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A = 44.42A = 44.42oo B = 18.54 B = 18.54oo C = C = 117.04117.04oo

551414

1111

AA

BBCC

Graphs

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It has an even degree and negative It has an even degree and negative leading coefficient.leading coefficient.

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The graph of a polynomial falls to both The graph of a polynomial falls to both the left and right. What can we tell the left and right. What can we tell about the polynomial?about the polynomial?

5 Point Question5 Point Question

10 Point Question10 Point Question

Sketch the graph of y = 3cos(2x) – 5. Sketch the graph of y = 3cos(2x) – 5.

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period is Pi, amplitude is 3, period is Pi, amplitude is 3, midline midline

is -5. It starts at (0,-2).is -5. It starts at (0,-2).

25 Point Question25 Point Question

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Find the equation for a sine function that matches the graph below.

Y = 2sin(x-π/4) +4

(π/4, 4)(π/4, 4) (9π/4,4)(9π/4,4)

Find the equation for the polynomial Find the equation for the polynomial function graphed below.function graphed below.

50 Point Question50 Point Question

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Y = -2(x-3)(x+1)Y = -2(x-3)(x+1)22

(0,6)(0,6)

Find the equation for the rational Find the equation for the rational function graphed below.function graphed below.

100 Point Question100 Point Question

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Y = -2(xY = -2(x22-9)/(x-9)/(x22-x-2)-x-2)(0,-9)(0,-9)

Polar Form

Plot the polar point (3, 150Plot the polar point (3, 15000).).

5 Point Question5 Point Question

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3030oo

• 33

Convert the point (-8,-6) to Convert the point (-8,-6) to polar coordinates.polar coordinates.

10 Point Question10 Point Question

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(10, 216.9(10, 216.900))

-67.29i + 251.14j-67.29i + 251.14j

A plane flies N 15A plane flies N 1500 W at a speed of 260 W at a speed of 260 miles per hour. Write the plane’s velocity miles per hour. Write the plane’s velocity vector in component form.vector in component form.

25 Point Question25 Point Question

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50 Point Question50 Point Question

Write the complex number 5 – 3i in Write the complex number 5 – 3i in polar form.polar form.

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)54.0sin()54.0cos(34 i

Compute (1 – i)Compute (1 – i)1/31/3. Write your . Write your answer in polar form.answer in polar form.

221/6 1/6 ee--ππi/12i/12

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Functions

A power functionA power function

5 Point Question5 Point Question

What type of function is this? What type of function is this? F(x) = 3x F(x) = 3x-2-2

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Find the equation for the power function Find the equation for the power function that passes through (1, 5) and (5, 1/25)that passes through (1, 5) and (5, 1/25)

10 Point Question10 Point Question

F(x) = 5xF(x) = 5x-3-3

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Graph the polynomial f(x) = 3(x - 3)Graph the polynomial f(x) = 3(x - 3)33 (x + (x + 20), labeling all zeros, y-intercepts and 20), labeling all zeros, y-intercepts and

asymptotes.asymptotes.

25 Point Question25 Point Question

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(3,0), (-20,0), (0,-1620)(3,0), (-20,0), (0,-1620)

50 Point Question50 Point Question

Asymptotes y = 0, x=2, and x=-5,Asymptotes y = 0, x=2, and x=-5,(which doesn’t show well)(which doesn’t show well)

Intercept Points: (-4,0),(0,1/5)Intercept Points: (-4,0),(0,1/5)

Sketch the graph ofSketch the graph of

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)5()2(

42 xx

xy

(-4,0)(-4,0)

100 Point Question100 Point Question

Find the exact value of Find the exact value of coscos-1-1(cos(28(cos(28ππ/25))./25)).

2222ππ/25/25

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Leftovers

U = 3i – 5 j, V = 4i – 2j. Find the U = 3i – 5 j, V = 4i – 2j. Find the dot product of the vectors U and V.dot product of the vectors U and V.

5 Point Question5 Point Question

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2222

What is the equation for a rose curve What is the equation for a rose curve with 8 petals of length 3.with 8 petals of length 3.

10 Point Question10 Point Question

R=3cos(4R=3cos(4ΘΘ))

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25 Point Question25 Point Question

Solve the equation: tan(2Solve the equation: tan(2ΘΘ) = √3.) = √3.

ΘΘ = = ππ/6 + /6 + ππk/2k/2

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50 Point Question50 Point Question

Solve the equation: Solve the equation: sin(x) + 2cossin(x) + 2cos22(x) = 2(x) = 2

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x = x = ππk, k, ππ/6 + 2/6 + 2ππk, k, 55ππ/6 + 2/6 + 2ππkk

Verify the identity: Verify the identity: 100 Point Question100 Point Question

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sure enough…sure enough…

)sec()cos()tan()sin( xxxx

Cable on right: Cable on right: 222 lbs. 222 lbs.

Cable on left: Cable on left: 141.8 lbs 141.8 lbs 

A 235 lb weight is suspended by two cables A 235 lb weight is suspended by two cables as shown in the diagram. Find the force in as shown in the diagram. Find the force in each cable.each cable.

Final QuestionFinal Question

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235 lbs235 lbs

5454oo2323oo