2. TrianglesTriangles 100 50 25 10 5GraphsGraphs Polar Form FunctionsFunctions LeftoversLeftovers Review for the Final 100 50 25 10 5 100 50 25 10 5 100 50 25 10 5 100 50 25 10 5 The 104 Challenge Review for the Final Final Round

3. Triangles

4. CheckWork In any right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. Go Home Go Home 5 Point Question What is the Pythagorean Theorem?

5. In the triangle ABC, C = 90 o, A = 25 o and a = 3. Find b. 10 Point Question CheckWork Go Home Go Home b = 6.433

6. 11.49 25 Point Question Find c in the triangle below: CheckWork Go Home Go Home 12 cm c 38 o 102 o

7. 13.099 cm 50 Point Question Find the length of the missing side in the triangle below. CheckWork Go Home Go Home 68 o 13 cm 10 cm

8. Find all three missing angles in the triangle below. 100 Point Question CheckWork Go Home Go Home A = 44.42 o B = 18.54 o C = 117.04 o 5 14 11 A B C

9. Graphs

10. CheckWork It has an even degree and negative leading coefficient. Go Home Go Home The graph of a polynomial falls to both the left and right. What can we tell about the polynomial? 5 Point Question

11. 10 Point Question Sketch the graph of y = 3cos(2x) – 5. CheckWork Go Home Go Home period is Pi, amplitude is 3, midline is -5. It starts at (0,-2).

12. 25 Point Question CheckWork Go Home Go Home Find the equation for a sine function that matches the graph below. Y = 2sin(x-π/4) +4 (π/4, 4) (9π/4,4)

13. Find the equation for the polynomial function graphed below. 50 Point Question CheckWork Go Home Go Home Y = -2(x-3)(x+1) 2 (0,6)

14. Find the equation for the rational function graphed below. 100 Point Question CheckWork Go Home Go Home Y = -2(x 2 -9)/(x 2 -x-2) (0,-9)

15. Polar Form

16. Plot the polar point (3, 150 0 ). 5 Point Question CheckWork Go Home Go Home 30 o 3

17. Convert the point (-8,-6) to polar coordinates. 10 Point Question CheckWork Go Home Go Home (10, 216.9 0 )

18. -67.29i + 251.14j A plane flies N 15 0 W at a speed of 260 miles per hour. Write the plane’s velocity vector in component form. 25 Point Question CheckWork Go Home Go Home

19. 50 Point Question Write the complex number 5 – 3i in polar form. CheckWork Go Home Go Home

20. Compute (1 – i) 1/3. Write your answer in polar form. 2 1/6 e -πi/12 100 Point Question CheckWork Go Home Go Home

21. Functions

22. A power function 5 Point Question What type of function is this? F(x) = 3x -2 CheckWork Go Home Go Home

23. Find the equation for the power function that passes through (1, 5) and (5, 1/25) 10 Point Question F(x) = 5x -3 CheckWork Go Home Go Home

24. Graph the polynomial f(x) = 3(x - 3) 3 (x + 20), labeling all zeros, y-intercepts and asymptotes. 25 Point Question CheckWork Go Home Go Home (3,0), (-20,0), (0,-1620)

25. 50 Point Question Asymptotes y = 0, x=2, and x=-5, (which doesn’t show well) Intercept Points: (-4,0),(0,1/5) Intercept Points: (-4,0),(0,1/5) Sketch the graph of CheckWork Go Home Go Home (-4,0)

26. 100 Point Question Find the exact value of cos -1 (cos(28π/25)). 22π/25 CheckWork Go Home Go Home

27. Leftovers

28. U = 3i – 5 j, V = 4i – 2j. Find the dot product of the vectors U and V. 5 Point Question CheckWork Go Home Go Home22

29. What is the equation for a rose curve with 8 petals of length 3. 10 Point Question R=3cos(4Θ) CheckWork Go Home Go Home

30. 25 Point Question Solve the equation: tan(2Θ) = √3. Θ = π/6 + πk/2 CheckWork Go Home Go Home

31. 50 Point Question Solve the equation: sin(x) + 2cos 2 (x) = 2 CheckWork Go Home Go Home x = πk, π/6 + 2πk, 5π/6 + 2πk

32. Verify the identity: 100 Point Question CheckWork Go Home Go Home sure enough…

33. Cable on right: 222 lbs. Cable on left: 141.8 lbs Cable on left: 141.8 lbs A 235 lb weight is suspended by two cables as shown in the diagram. Find the force in each cable. Final Question CheckWork Go Home Go Home 235 lbs 54 o 23 o