Algebra 3 Final Exam Study Guide

1 / Find the radian measure of the angle:
2 / Find the degree measure of the angle:
3 / Find the degree measure of the angle: .
4 / The measure of the angle in standard position is given. Find minimal positive angle and maximal negative angles that are coterminal with the given angle.
5 / The measure of the anglein standard position is given. Find the minimal positive angle and the maximal negative angle that is coterminal with the given angle.
6 / Find the length of the arc s in the figure if radius R = 8 and angle a = 100 o.

7 / Find and if x = 5, and y = 1.

8 / A water tower is located x = 315 ft from a building (see the figure). From a window in the building it is observed that the angle of elevation to the top of the tower is 39 and the angle of depression to the bottom of the tower is 25 . How tall is the tower? How high is the window?

9 / Find x, correct to one decimal place.

y = 115
10 / Find x, correct to one decimal place.

y = 60
11 / Use the Law of Sines to find x. Let .

12 / Use the Law of Sines to find x. Let .

13 / Use the Law of Sines to find angle C. Let a = 28, and c = 11.

14 / A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, c = 7 mi apart, to be
(a) Find the distance of the plane from point A.
(b) Find the elevation of the plane.

15 / Find the indicated angle . (Use either the Law of Sines or the Law of Cosines, as appropriate.)

(a = 120, c = 135, )
16 / A triangular field has sides of lengths 22, 32, and 48 yd. Find the largest angle. Round to the nearest tenth.
17 / Use the substitution method to find all solutions of the system of equations
y = x²
y = x + 6
18 / Use the elimination method to find all solutions of the system of equations
5x² - y² = 4
x² + 8y² = 9
19 / Find all solutions of the system of equations
y + x² = 6x
y + 6x = 36
20 / Find all solutions of the system of equations
x - y = 1
xy = 12
21 / Solve the system or show that it has no solution.
-3x + 2y = 16
2x + 3y = -2
If the system has infinitely many solutions, express your answer as an ordered pair in the form ( t , f ( t ) ) , where x = t and y = f ( t ).
22 / Solve the system, or show that it has no solution.
12x - 36y = 12
-9x + 27y = 9
If the system has infinitely many solutions, express your answer as an ordered pair in the form ( t , f ( t ) ) , where x = t and y = f ( t ).
23 / Use back - substitution to solve the triangular system.
5x - y + 4z = 14
y + 8z = 0
- 2z = 1
24 / Find the complete solution of the linear system.
X + y - z = 0
X + 2y - 7z = -2
2x + 3y - 8z = -2
25 / Solve the system of linear equations.
2x -3y + z = -8
-4x +y -3z = 10
x - y +4z = 0
26 / Multiply together matrixand matrix
27 / Find AB + AC, if
, and
28 / Solve the matrix equation 3 X - A = B for the unknown matrix X , if
and
29 / Solve the matrix equation 3( X - B ) = A for the unknown matrix X, if
and
30 / Use Cramer's Rule to solve the system.
4X - 7Y + Z = 0
8X + 2Z = 70
-X + 2Y = 0

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