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Chapter 13.1-13.5-Bradshaw Algebra 2 w/trig Test
Short Answer
1. Find the values of the six trigonometric functions for angle
, when AC = 10 and BC = 8.
2. Find the values of the six trigonometric functions for angle
, when PQ = 60 and QR = 80.
3. Solve ABC by using the measurements
,
the nearest tenth and measures of angles to the nearest degree.
, and
. Round measures of sides to
4. Solve ABC by using the measurements
,
the nearest tenth and measures of angles to the nearest degree.
, and
. Round measures of sides to
5. A 15-m long ladder rests against a wall at an angle of
from the wall?
with the ground. How far is the foot of the ladder
6. The upper part of a tree, broken by wind, makes an angle of 38 with the ground. The horizontal distance
from the root of the tree to the point where the top of the tree meets the ground is 20 meters. Find the height
of the tree before it was broken.
Rewrite the radian measure in degrees.
7.
8.
Rewrite the degree measure in radians.
9. –1080°
10. 9°
11. Find one angle with positive measure and one angle with negative measure coterminal with an angle of 172°.
Find the value of the given trigonometric function.
12. sin –585
13. cos 780
14. cot 210
Find the exact values of the remaining five trigonometric functions of .
15. Suppose
is an angle in the standard position whose terminal side is in Quadrant III and
.
16. Suppose
is an angle in the standard position whose terminal side is in Quadrant IV and
17. Suppose
is an angle in the standard position whose terminal side is in Quadrant II and
.
.
Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the
nearest degree.
18.
c = 9.0, B = 40°, C = 65°
19.
Q = 35°, p = 8, q = 5
Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle.
Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
20.
A =115°, a = 7, b = 4
21.
P = 38°, p = 8, q = 6.
Determine whether each triangle should be solved by beginning with the Law of Sines or the Law of Cosines.
Then solve each triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest
degree.
22.
A = 75 , b = 8, a = 13
23.
A = 75 , b = 11, a = 14
The given point P is located on the unit circle. Find sin
and cos .
24. P(0.8, 0.6)
25. P
Chapter 13.1-13.5-Bradshaw Algebra 2 w/trig Test
Answer Section
SHORT ANSWER
1. ANS:
4
3
5
5
4
3
= , cos = , csc = , sec = , tan = , and cot = .
5
5
4
3
3
4
If is the measure of an acute angle of a right triangle, opp is the measure of the leg opposite , adj is the
measure of the leg adjacent to , and hyp is the measure of the hypotenuse, then the following are true.
sin
sin
cos
tan
csc
sec
cot
KEY: Trigonometric Functions, Acute Angles
NOT: /A/ Did you use the correct definition of trigonometric ratios? /B/ The sine, cosine, and tangent
functions are reciprocals of the cosecant, secant, and cotangent functions, respectively. /C/ If x is the measure
of an acute angle of a right triangle, then opp is the measure of the leg opposite x, adj is the measure of the leg
adjacent to x, and hyp is the measure of the hypotenuse./D/ Correct!
2. ANS:
4
3
5
5
4
3
sin = , cos = , csc = , sec = , tan = , and cot = .
5
5
4
3
3
4
If is the measure of an acute angle of a right triangle, opp is the measure of the leg opposite , adj is the
measure of the leg adjacent to , and hyp is the measure of the hypotenuse, then the following are true.
sin
cos
tan
csc
sec
cot
KEY: Trigonometric Functions, Acute Angles
NOT: /A/ Correct! /B/ If x is the measure of an acute angle of a right triangle, then opp is the measure of the
leg opposite x, adj is the measure of the leg adjacent to x, and hyp is the measure of the hypotenuse./C/ The
sine, cosine, and tangent functions are reciprocals of the cosecant, secant, and cotangent functions,
respectively. /D/ Did you use the correct definition of trigonometric ratios?
3. ANS:
,
,
If the measures of one side and one acute angle are known, you can determine the measures of all sides and
angles of the triangle by using trigonometric functions.
KEY: Solve Triangles, Right Triangles
NOT: /A/ Did you interchange the values of b and c? /B/ Correct! /C/ Use the measures of one side and one
acute angle to find the other measures./D/ Did you use the trigonometric functions to find the missing
measures?
4. ANS:
,
,
If the measures of one side and one acute angle are known, you can determine the measures of all sides and
angles of the triangle by using trigonometric functions.
KEY: Solve Triangles, Right Triangles
NOT: /A/ Did you use the trigonometric functions to find the missing measures? /B/ Correct!/C/ Did you
interchange the values of p and q? /D/ Use the measures of the side and acute angle to find the missing
measures.
5. ANS:
7.5 m
Write an equation using a trigonometric function that involves the ratio of length and 15.
KEY: Right Triangles, Real-World Problems
NOT: /A/ Correct! /B/ Did you write an equation using a trigonometric function that involves the ratio of the
length of the ladder and the distance of the foot of the ladder from the wall? /C/ Use cos 60 to find how far is
the foot of the ladder from the wall. /D/ Did you use the correct trigonometric function?
6. ANS:
41.006 m
Write an equation using a trigonometric function that involves the ratio of and 20.
KEY: Right Triangles, Real-World Problems
NOT: /A/ Did you use the correct trigonometric function? /B/ Did you write an equation using a
trigonometric function? /C/ Use the tan function to find the height of the lower part of the tree. /D/ Correct!
7. ANS:
10
To rewrite the radian measure of an angle in degrees, multiply the number of radians by
.
KEY: Radian Measure, Degree Measure
NOT: /A/ One radian is around 57 degrees. /B/ Did you multiply the number of radians correctly by the
conversion factor? /C/ One degree is about 0.0175 radian. /D/ Correct!
8. ANS:
45
To rewrite the radian measure of an angle in degrees, multiply the number of radians by
.
KEY: Radian Measure, Degree Measure
NOT: /A/ One degree is about 0.0175 radian. /B/ One radian is about 57 degrees. /C/ Correct!/D/ Did you
multiply the number of radians correctly by the conversion factor?
9. ANS:
To rewrite the degree measure of an angle in radians, multiply the number of degrees by
.
KEY: Radian Measure, Degree Measure
NOT: /A/ Did you multiply the number of degrees correctly by the conversion factor? /B/ One degree is
about 0.0175 radian. /C/ One radian is about 57 degrees./D/ Correct!
10. ANS:
To rewrite the degree measure of an angle in radians, multiply the number of degrees by
.
KEY: Radian Measure, Degree Measure
NOT: /A/ One degree is about 0.0175 radians. /B/ Did you multiply the number of degrees correctly by the
conversion factor? /C/ Correct! /D/ One radian is about 57 degrees.
11. ANS:
532°, –188°
In degree measure, coterminal angles differ by an integral multiple of 360 .
KEY: Coterminal Angles
NOT: /A/ In degree measure, coterminal angles differ by an integral multiple of 360 degrees. /B/ Correct! /C/
When two angles in the standard position have the same terminal sides, they are called coterminal angles. /D/
Did you add or subtract the given angle with an integral multiple of 360 degrees?
12. ANS:
First, find the reference angle . Then, find the value of the trigonometric function for . Then, using the
quadrant in which the terminal side of lies, determine the sign of the trigonometric function value of .
KEY: Sine, Cosine
NOT: /A/ Did you find the reference angle of the given angle?/B/ Use a reference angle to find the value of
the given trigonometric function. /C/ Correct! /D/ Find the sine of the given angle, not tan.
13. ANS:
First, find the reference angle . Then, find the value of the trigonometric function for . Then, using the
quadrant in which the terminal side of lies, determine the sign of the trigonometric function value of .
KEY: Sine, Cosine
NOT: /A/ Use a reference angle to find the value of the given trigonometric function. /B/ Find the cos of the
given angle, not tan. /C/ Did you find the reference angle of the given angle?/D/ Correct!
14. ANS:
First, find the reference angle . Then, find the value of the trigonometric function for . Then, using the
quadrant in which the terminal side of lies, determine the sign of the trigonometric function value of .
KEY: Tangent, Cotangent
NOT: /A/ Use a reference angle to find the value of the given trigonometric function. /B/ Correct!/C/ Find
the cot of the given angle, not tan. /D/ Did you find the reference angle of the given angle?
15. ANS:
sin
, csc
, sec
, tan
, and cot
If the quadrant that contains the terminal side of in the standard position and the exact value of one
trigonometric function of are known, then the values of the other trigonometric functions of can be
obtained using the function definitions.
KEY: Reference Angles, Trigonometric Functions
NOT: /A/ Did you use the correct signs of the trigonometric functions for Quadrant III? /B/ The angle is in
Quadrant III and not in Quadrant II. /C/ Use function definitions to find the remaining five trigonometric
functions. /D/ Correct!
16. ANS:
cos
, csc
, sec
, tan
, cot
If the quadrant that contains the terminal side of in the standard position and the exact value of one
trigonometric function of are known, then the values of the other trigonometric functions of can be
obtained using the function definitions.
KEY: Reference Angles, Trigonometric Functions
NOT: /A/ Correct! /B/ The angle is in Quadrant IV and not in Quadrant I. /C/ Did you use the correct signs of
the trigonometric functions for Quadrant IV? /D/ Use function definitions to find the remaining five
trigonometric functions.
17. ANS:
cos
, csc
, sec
, tan
, cot
If the quadrant that contains the terminal side of in the standard position and the exact value of one
trigonometric function of are known, then the values of the other trigonometric functions of can be
obtained using the function definitions.
KEY: Reference Angles, Trigonometric Functions
NOT: /A/ The angle is in Quadrant II and not in Quadrant I. /B/ Use function definitions to find the
remaining five trigonometric functions. /C/ Did you use the correct signs of the trigonometric functions for
Quadrant II? /D/ Correct!
18. ANS:
A = 75°, a = 9.6, b = 6.4
Let
be any triangle with , , and representing the measures of sides opposite angles with
measurements , , and respectively. Then,
KEY: Solve Problems, Law of Sines
NOT: /A/ Correct! /B/ Did you interchange the values of the sides? /C/ Apply the Law of Sines to solve the
triangle./D/ Did you apply the Law of Sines to solve the triangle?
19. ANS:
P = 90°, R = 55°, r = 6.6
Let
be any triangle with , , and representing the measures of sides opposite angles with
measurements , , and
respectively. Then,
.
KEY: Solve Problems, Law of Sines
NOT: /A/ Did you apply the Law of Sines to solve the triangle? /B/ Correct! /C/ Did you interchange the
values of the sides? /D/ Apply the Law of Sines to solve the triangle.
20. ANS:
one solution; c 4.0; B 31°; C 34°
Determine whether the given triangle has zero, one or two solutions. Find the measure of angle C and the
value of c.
KEY: Solve Triangles
NOT: /A/ Did you interchange the values of angles B and C?/B/ Correct! /C/ Did you calculate the value of C
correctly? /D/ Did you use the Law of Sines correctly?
21. ANS:
one solution; r 8.0; Q
; R 115
Find whether the given triangle has one, two or zero solution and then find the values asked in the question by
applying appropriate formula.
KEY: Solve Triangles
NOT: /A/ The sum of the measures of the angles of a triangle is 180./B/ Correct! /C/ Did you use the Law of
Sines? /D/ Did you find the value of r and the corresponding angle correctly?
22. ANS:
Law of Sines; B 37 , C 69 , c 13.0
Use the Law of Sines when two sides and an angle opposite one of them are given.
KEY: Solve Triangles, Law of Sines, Law of Cosines
NOT: /A/ What is the Law of Sines?/B/ Did you use the correct law? /C/ Did you interchange the angles? /D/
Correct!
23. ANS:
Law of Sines; B 49 , C 56 , c 12.0
Use the Law of Sines when two sides and an angle opposite one of them are given.
KEY: Solve Triangles, Law of Sines, Law of Cosines
NOT: /A/ Did you use the correct law? /B/ What is the Law of Sines?/C/ Correct! /D/ Did you interchange
the angles?
24. ANS:
sin = 0.6; cos = 0.8
If the terminal side of an angle in the standard position intersects the unit circle at P(x, y), then cos = x
and sin = y.
KEY: Trigonometric Functions, Unit Circle
NOT: /A/ Correct! /B/ Did you write the answers in the correct order? /C/ Did you change the sign of the
coordinates? /D/ Check the sign of the coordinates.
25. ANS:
sin
=
; cos
=
If the terminal side of an angle
and sin = y.
in the standard position intersects the unit circle at P(x, y), then cos
=x
KEY: Trigonometric Functions, Unit Circle
NOT: /A/ Did you write the answers in the correct order? /B/ Correct! /C/ Did you change the sign of the
coordinates? /D/ Check the sign of the coordinates.