Semester 2 Final Review 2017 Name:______
1. Find the exact functional value.
a. sin-1 1 b. cos-1 -32 c. tan-1 1 d. sin-1 22
2. Determine if fx and g(x) are inverses of each other, must show work. fx=2x-6 gx=x2+3
3. State the domain and range of the following inverse trig functions
a. cos-1x 3. a. Domain:______
Range:______
b. sin-1x b. Domain:______
Range:______
c. tan-1x c. Domain:______
Range:______
For problems 4-9, solve the equations on the domain [0, 2π):
4. secx=-2 5. 3tan2x-1=0
6. 2cosx+1=0 7. tanx sinx=sinx
8. 2sin2x+sinx-1=0 9. sec2x+tanx=3
Use the addition or subtraction identities to evaluate the given expression exactly.
10. sin13π12 11. cosπ12 12. tan5π12
Find sin 2x, cos 2x, and tan 2x under the given conditions
13. secx=-53 (π<x<3π2) 14. cotx=-23 (π2<x<π)
15. Write the complex number in standard form:
a) i2 + 3i b) 3 - c) 6 + d)
16. Perform the operations and write in standard form:
a) b) i(6 + i)(3 – 2i) c)
d) (7+ 5i) + (-4 + 2i) e) (7+ 5i) - (-4 + 2i) f) Evaluate
17. Find all of the solutions:
a) 3x2 + 1 = 0 b) x2 -2x + 10 = 0 c) x2 – x = 0
d) x2 + 8x + 10 = 0
In exercises 18-19, write the complex number in polar form. You may want to sketch it to help you locate the angle. Use radians in your answers.
18.
Polar form: ______
19.
Polar form: ______
For problems 20-22, write the expression in complex standard form.
20.
21.
22.
23. If and find:
a) b)
24. If and z = -10i find:
a) b)
25. Write the component form the vector.
S (-4,3) Y (-6, -3)
Use the following information to answer questions 26 and 27.
v = < -4,- 2 > u = < 7, -4 > w = 3i – 8j
26. 3v + 2u
27.( u • v)(u • w)
Are the following orthogonal, parallel, or neither
28. u= <-2,2> ; v= <1,1>
29. u= <1,4> ; v= <2,8>
30. Write the component form of v given the magnitude and angle it makes with the positive x-axis.
31. Find the unit vector of:
u = 6i-2j
32. Find the direction angle of the given vector. (quadrant!!!)
u = -4i + -3j
33. Find the angle between the two vectors.
a)
State the transformations that have occurred from the parent graphs.
1. a) b)
2.a) b)
Rewrite the equation in exponential form.
3. 4. 5. 6.
Simplify as much as possible.
7. 8. 9. 10.
11. 12. 13. 14.
15. 16. 17. 18.
19. 20. 21. 22.
23. 24. 25. 26.
Expand.
27. 28. , y > 1 29. 30.
Condense.
31. 32.
33. 34.
CALCULATOR
Solve.
36. 37. 38. 39.
40. 41. 42. 43.
44. 45. 46.
47. 48.
You deposit $1200 in an account that pays 5% annual interest. After 10 years you withdraw the money
49. Find the balance in the account if the interest was compounded quarterly.
50. Find the balance in the account if the interest was compounded continuously.
51. You deposit $2000 into an account that pays 2% annual interest compounded quarterly. How long will it take for the balance to increase by $500?
52. There is 29% of C-14 left in an ancient artifact discovered in Greece. If the half-life of C-14 is 5730 years, how old is the artifact?
53. The first permanent English colony in America was established in Jamestown, Virginia, in 1607. From 1620 to 1780, the population P of colonial America can be modeled by the equation where t is the number of years since 1620. When was the population of colonial America about 345,000?