2. IdentitiesIdentities 100 50 25 10 5ComponentsComponents EquationsEquations ApplicationsApplications AdditionAddition Math 104 – Review for Test #3 100 50 25 10 5 100 50 25 10 5 100 50 25 10 5 FINAL 50 25 10 5

3. Identities

4. CheckWork Go Home Go Home 5 Point Question Is the following an equation or an identity? Equation

5. CheckWork Go Home Go Home 10 Point Question Verify the identity: Replace sec(x) with 1/cos(x), then multiply by (sin(x)/sin(x)).

6. CheckWork Go Home Go Home 25 Point Question Verify the identity Use cos(2x)=cos 2 (x)-sin 2 (x) and factor.

7. CheckWork Go Home Go Home 50 Point Question Keep Score Keep Score Verify the identity: Convert to sines and cosines, use the Pythagorean identity twice.

8. CheckWork Go Home Go Home 100 Point Question Verify the identity: (cot(x) + cot(y)) sin(x) sin(y) = sin(x+y) Convert cot(x) to cos(x)/sin(x), cot(y) to cos(y)/sin(y), distribute, cancel and you are done.

9. Components

10. CheckWork 4.91i – 3.44j Go Home Go Home A vector has magnitude of 6 and direction angle of 325°. Write the vector in component form. 5 Point Question Keep Score Keep Score

11. CheckWork Magnitude = 10 Direction angle = 306.9° Go Home Go Home 10 Point Question Keep Score Keep Score Find the magnitude and direction angle for the vector 6i - 8j

12. CheckWork Go Home Go Home 25 Point Question Keep Score Keep Score If u + v = 0, and u = -2i+5j, what is v? v=2i-5j

13. CheckWork Go Home Go Home Car A is traveling with velocity vector 21i + 35j. Car B is traveling wit velocity vector 40j. Which car is traveling faster? 50 Point Question Keep Score Keep Score Car A

14. CheckWork Go Home Go Home Given u x = -5 and  = 120°, find u y 100 Point Question Keep Score Keep Score u y = 8.66

15. Equations

16. CheckWork X=30 0 +360 0 k or 150 0 + 360 0 k Go Home Go Home Solve: sin(x) = 1/2 5 Point Question

17. CheckWork Go Home Go Home Solve the equation 5cos(x)-4=0 10 Point Question Keep Score Keep Score X=0.6435 + 2Pi k or X=-0.6435 + 2Pi k

18. CheckWork X=30 0 + 180 0 k Or x=-30 0 + 180 0 k Go Home Go Home Solve the equation 3tan 2 x-1=0 25 Point Question

19. CheckWork X=90 0 +180 0 k or 60 0 +360 0 k or - 60 0 +360 0 k Go Home Go Home Solve: cos(2x)-cos(x)=-1 50 Point Question

20. CheckWork Go Home Go HomeSolve: 2sin 2 (3x)-sin(3x)-1=0 100 Point Question Keep Score Keep Score

21. Applications

22. CheckWork -192.8i+229.8j Go Home Go Home 5 Point Question Keep Score Keep Score A scout travels 300 yards in the direction N40°W. Write this vector in component form.

23. CheckWork Go Home Go Home What third force is required to keep 2i + 3j and –4i +3j in check? 10 Point Question Keep Score Keep Score 2i – 6j

24. A boat travels S 50° W for 14 miles, then travels N 10° E for 5 miles. What course and distance must the boat travel to make it back to its starting point? CheckWork 10.66 mi at N67.5°E Go Home Go Home 25 Point Question Keep Score Keep Score

25. Go Home Go Home 50 Point Question Keep Score Keep ScoreCheckWork A plane is flying at 200 miles per hour in the direction S 15° E. The wind is blowing due north at 30 miles per hour. What is the true speed and direction of the plane? 171.2 mph S17.6ºE

26. CheckWork Go Home Go Home 100 Point Question Keep Score Keep Score A 200 lb weight is suspended by two cables in the drawing below. How big is the tension in each cable? 236.6 lbs 25°25°

27. Addition

28. CheckWork Go Home Go Home 5 Point Question Keep Score Keep Score U = 2i + 3j, V = -3i + 2j - 4k Find U + V. U + V = -i + 5j – 4k

29. CheckWork Go Home Go Home Sketch the sum of the two vectors. 10 Point Question Keep Score Keep Score

30. CheckWork -6.407i+1.046j Go Home Go Home 25 Point Question Keep Score Keep Score u has a magnitude of 8 and a direction angle of 150º. v has a magnitude of 3 and a direction angle of 280°. Find u + v.

31. CheckWork x = -2 and y = -3 or 3 Go Home Go Home Find x and y if (y 2 i + 4xj) + (– 9i + 8j) = 0 50 Point Question Keep Score Keep Score

32. CheckWork Go Home Go Home FINAL QUESTION Keep Score Keep Score776.457 lbs A 3000 lb car is parked on a 15° incline. What force is required to keep it from rolling down the incline?