Math 118 Exam 4 Practice Problems
Exam 4 will cover Chapters 3 and 4 (3.1-3.3 and 4.1-4.7) and will be on Friday, December 2.
My office hours: Mon 9:15 - 10:45, Wed 12:15 - 1:45, Thur 12:30 - 3:00, Fri 9:15 - 10:45 in Old Main 404
Drop in tutoring: 6-8 pm on Sunday, Monday, Tuesday, and Thursday in Zurn 213
1. Match each of the graphs below to the appropriate trigonometric function (not all functions will be used).
• 3 cos(x/2 + 1)
• 3 cos(2x)
• sec(x + π)
•
• − tan(x + π)
• 2 cos(x − π/2) + 1
• 3 sin(x)
• 3 sin(x/2)
π
2
tan(x)
• 3 sin(2x)
−10
4
4
4
2
2
2
−5
5
−10
10
−5
−10
10
−2
−2
(a)
5
−4
(b)
2. Sketch a graph of one period of the functions:
(a) 3 sin(4x)
(c) 2 tan(−x + π)
(b) cos(2x + π)
(d) −2 cos((x/4)) − 1
3. Given sin(θ) = 3/5 and cos(θ) = 4/5, find tan(θ),
csc(θ), sec(θ) and cot(θ)
5. Find a positive angle less that
coterminal with the given angle θ:
5
10
−2
(c)
−4
8. Expand as a sum of logarithms:
!
x3 y
(c) log4 (16/x)
(a) ln
!
2
5z
64
s
(d) log8 √
x−2
3x
3
(b) log4
y
9. Write as a single logarithm.
4. Find cos(θ) given that sin(θ) = 2/5.
360◦
−4
−5
or 2π that is
(a) θ = 820◦
(c) θ = −π/5
(b) θ = 27π/4
(d) θ = −410◦
6. Find the exact value of the following expressions
(a) cos(3π/4)
(c) tan(2π/3)
(b) sin(5π/6)
(d) cot(π/2)
(a) log(x) + log(x2 + 1) − log(3x)
(b) 4 ln(x − 2) − 5 ln(y)
(c) 6(ln(x − 3) − ln(y))
10. Find the exact value of the following expressions.
(a) sin(sin−1 (0.3))
(b) tan−1 (tan(4π/3))
!
1
−1
(c) sin
−
2
(d) tan−1 (1)
−1
(e) sin
√ !
3
2
7. Evaluate each expression.
(a) log9 (81)
(c) 6log6 (20)
(b) log16 (4)
(d) 5 ln(1)
11. Using a sketch of a right triangle, find the exact value
of the following expressions.
(a) sin(cos−1 (3/5))
(b) tan(cos−1 (−4/5))
Math 118 Exam 4 Practice Solutions
(b) − tan(x + π)
1. (a) 3 sin(2x)
−10
(c) 2 cos(x − π/2)
4
4
4
4
2
2
2
2
−5
10 −10
5
−5
−2
10 −10
−2
−4
2. (a)
5
−4
(c)
3. tan(θ) = 3/4, sec(θ) = 5/4, csc(θ) = 5/3, cot(θ) = 4/3
4.
√
21/5
5. (a) 100◦
(b) 3π/4
√
6. (a) −1/ 2
7. (a) 2
(c) 9π/5
(b) 1/2
(b) 1/2
(c)
(c) 20
√
3
(d) 310◦
(d) 0
(d) 0
8. (a) 3 ln(x) + ln(y) − ln(5) − 2 ln(z)
(b)
1
3
log4 (3) + 13 log4 (x) − 13 log4 (y)
(c) 2 − log4 (x)
(d) 2 − 21 log8 (x − 2)
9. (a) log
x3 + x
3x
10. (a) 0.3
!
(b) 4π/3
(b) ln
(x − 2)4
y5
(c) 5π/4
!
(c) ln
(d) π/4
x−3
y
!6
(e) π/3
11. (a) 4/5
(b) −3/4
Other facts you’ll want to know
1. How to convert between radian and degree measurements of angles
2. The value of all six trig functions at multiples of π/4, π/2, and π/6
3. The period, domain and range of the six trig functions
4. The value of ln(1)
5. The relationship between ex and ln(x)
5
10 −15
−10
−5
5
−2
−2
−4
(b)
−5
(d)
−4
10
15