Chapter 5 Review Problems

PreCalculus Chapter 5 Review Problems

1.) Change 135 to radian measure in terms of .

p 2.) Change - to degree measure. 5

7p 3.) Find the reference angle and all angles coterminal with 480 and . 12

3p 5.) Find the arc length of a circle with diameter 30 in and q = . 4

5p 7.) Find the area of the sector if q = and r = 10 ft. 12

8.) Find the values of the 6 trig functions if (3, -4) lies on the terminal side of an angle.

1 9.) Suppose sin x = Find cos x . 2

4 10.) Suppose sin x = - and the terminal side lies in quadrant IV. Find the other 5 trig functions. 5

11.) Find each exact value. p 5p a. csc90° b. cos60° c. sin d. cos 3 6

14.) Find the area of the triangle with A = 20°,a= 19,C = 64° Chapter 6 Review Problems

1. Graph y = sin x on -180 Ј x Ј 180° .

q 2. Graph y = 3cos 2

3. State the amplitude, phase shift, and period for each function.

a. y = 3cos4q b. y = 11tan(15q - 45°)

4. Evaluate each expression. Assume all angles are in quadrant I.

ж 3 ц -1 5 -1 3 sin arccos tanжcos ц cosжtan ц a. з ч b. з ч c. з ч и 2 ш и 13ш и 4 ш

ж 2ц d. cos(arctan 3 + arccot 3) e. tan p + Arcsin из 3шч

5. Write the equation of a cosine function with amplitude=3, period=180, and phase shift=120. Chapter 7 Review Problems

1. Solve for all values. 1 a. If cot x = 2, find tan x. b. If sin x = , find cosx. 2

2. Express each value as a function of an angle in quadrant I. a. sin665° b. tan(-342°)

3. Simplify. tan x csc x cos2 x a. b. c. sin2 x cos2 x + sin4 x sec x 1+ sin x

1+ tan x 4. Verify: a. sin x + cosx = b. 1+ sec2 xsin2 x = sec2 x secx

6. Solve each equation.

a. 2 cos x - 1 = 0 b. sin2 x - 3sin x + 2 = 0 c. 2cos2 x = sin x + 1

Chapter 9 Review Problems 1. Find the polar coordinates of (-3,-3)

2. Name the classical curve given by r = 3cos2q

o 3. Find the rectangular coordinates of the point (4,135 )

4. Simplify: i30

5. Multiply (3 + 2i)(4 - 5i)

6. Write in complex polar form : 2 - 2i

o o 7. Write in complex rectangular form : 2(cos60 + isin60 )

Chapter 10 Review Problems 1. Find the focus, vertex, and equations of the directrix and axis of symmetry of y2 -12 - 16 x - 4 y = 0

2. Write the standard for the ellipse: 4x2+ 9 y 2 + 16 x - 36 y = - 16

3. Find the foci, center, and vertices of 12x2+ 24 x - 12 y 2 + 48 y = 48 . Find the equations of the asymptotes.

4. Write the standard form of the parabola whose directrix is x= -4 and whose focus is at (2,3).

x2+ y 2 = 4 5. Solve the following system of equations. y=2 x - 1

6. Identify the conic section represented by 3y2- 3 x 2 + 12 y + 18 x = 42

7 Write the standard form of the ellipse with foci at ( 4,0) and whose semi-minor axis is 5 units long.

8. Write the standard form of the circle x2+ y 2 +2 x - 2 y = 2

Chapter 12 Review Problems 1. Find the 35th term in the sequence -5, -1, 3, …

2. Form a sequence that has three arithmetic means between 6 and -4.

3. Find the ninth term of the sequence -8, -4, -2, -1, …

4. Form a sequence that has three geometric means between 0.2 and 125.

5. Evaluate each limit or state that the limit does not exist.

2n (-1)n n2 4n3 - 3n lim a. b. lim 2 c. lim 4 3 n®Ҙ 5n + 1 n®Ҙ 5n n®Ҙ n - 4n

6. Write in expanded form and find the sum.

11 Ҙ a. (2a - 4) b. (0.4)k еa=5 еk =1

7. Express each series using sigma notation.

a. -1 + 1 + 3 + 5 + … b. 2 + 5 + 10 + 17 + … + 82

8. Expand (2r + 3s)4

9. Find the fifth term of (x - 1)15