algebra final
Name/Student Number:
Algebra 2 Final Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the trigonometric expression. 1.
a.
b.
c.
d.
Answer B
In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. 2. a = 3, c = 19
a.
= 9.1°, = 80.9°, b = 18.8
c.
= 14.5°, = 75.5°, b = 18.8
b.
= 80.9°, = 9.1°, b = 18.8
d.
= 75.5°, = 14.5°, b = 18.8
Answer A
3.
What is the simplified form of sin(x + p)?
a.
cos x
b.
sin x
c.
–sin x
d.
–cos x
Answer C Rewrite the expression as a trigonometric function of a single angle measure. 4.
a.
b.
c.
d.
Answer A
Short Answer 5.
Consider the sequence 1, , , , ,...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
6.
Consider the sequence 16, –8, 4, –2, 1, ...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
7.
Consider the graph of the cosine function shown below.
a. Find the period and amplitude of the cosine function.
b. At what values of for do the maximum value(s), minimum values(s), and zeros occur?
Verify the identity. Justify each step. 8.
sinΘ/cosΘ+cosΘ/sinΘ sin^20+cos^2Θ/sinΘcosΘ 1/sinΘcosΘ 9.
Verify the identity .
cot ( Θ - π / 2 )= cos ( Θ - π / 2 ) / sin ( Θ - π / 2 )
cos ( Θ - π / 2 )= cos(Θ) cos (π/2) + sin(Θ) sin (π/2) = cosΘ (0) + sinΘ (1) = sinΘ
sin ( Θ - π / 2 )= sinΘ cos(π/2) - cosΘ sin(π/2) = sinΘ (0) - cosΘ (1) = -cosΘ so you get, cot ( Θ - π / 2 )= sinΘ / -cosΘ cot ( Θ - π / 2 )= -tanΘ 10.
Use the definitions of the trigonometric ratios for a right triangle to derive a
Algebra 2 Final Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the trigonometric expression. 1.
a.
b.
c.
d.
Answer B
In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. 2. a = 3, c = 19
a.
= 9.1°, = 80.9°, b = 18.8
c.
= 14.5°, = 75.5°, b = 18.8
b.
= 80.9°, = 9.1°, b = 18.8
d.
= 75.5°, = 14.5°, b = 18.8
Answer A
3.
What is the simplified form of sin(x + p)?
a.
cos x
b.
sin x
c.
–sin x
d.
–cos x
Answer C Rewrite the expression as a trigonometric function of a single angle measure. 4.
a.
b.
c.
d.
Answer A
Short Answer 5.
Consider the sequence 1, , , , ,...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
6.
Consider the sequence 16, –8, 4, –2, 1, ...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
7.
Consider the graph of the cosine function shown below.
a. Find the period and amplitude of the cosine function.
b. At what values of for do the maximum value(s), minimum values(s), and zeros occur?
Verify the identity. Justify each step. 8.
sinΘ/cosΘ+cosΘ/sinΘ sin^20+cos^2Θ/sinΘcosΘ 1/sinΘcosΘ 9.
Verify the identity .
cot ( Θ - π / 2 )= cos ( Θ - π / 2 ) / sin ( Θ - π / 2 )
cos ( Θ - π / 2 )= cos(Θ) cos (π/2) + sin(Θ) sin (π/2) = cosΘ (0) + sinΘ (1) = sinΘ
sin ( Θ - π / 2 )= sinΘ cos(π/2) - cosΘ sin(π/2) = sinΘ (0) - cosΘ (1) = -cosΘ so you get, cot ( Θ - π / 2 )= sinΘ / -cosΘ cot ( Θ - π / 2 )= -tanΘ 10.
Use the definitions of the trigonometric ratios for a right triangle to derive a