Math 1613, L. Brown
Section 1.4: Right Triangle Applications
Right triangle ratios can be used to solve application problems involving right
triangles.
sin =
opposite
hypotenuse
adjacent
cos =
hypotenuse
tan =
opposite
adjacent
hypotenuse
opposite
adjacen
Math 1613, L. Brown
Section 2.1: Degrees and Radians
Radian Measure
One radian (rad) is the measure of the central angle
formed when the arc length equals the radius of the
circle.
2 radians = 360 (a full revolution)
radians = 180 (a half revolution)
One
Math 1613, L. Brown
Section 2.3: Unit Circle Approach
Note: In this section of the notes, we will use a letter t to represent an angle. The
textbook uses an x for this angle.
A unit circle is a circle of radius 1. A point (a, b) is on the unit circle only
Math 1613, L. Brown
Section 2.5: Exact Values and Properties of Trig Functions
Quadrantal Angles
A quadrantal angle is an angle which lies on either the x-axis or the y-axis.
Example 1
Find the points on the unit circle corresponding to the
3
angles and
.
Trigonometry Fall 2012 Sample Quiz 5
This quiz concerns the function displayed in the following graph.
1
4
3
2
1
1
2
3
4
1
2
3
1. [2 points] What is the vertical shift of this function?
2. [2 points] What is the amplitude of this function?
3. [2 points] W
Trigonometry Fall 2012 Sample Quiz 2
In Problem 4, you must show your method to receive credit.
1. [2 points] Use a calculator to nd the cosine of 3.7 . Round your answer to three
decimal places.
2. [2 points] Use a calculator to nd the cotangent of 10 .
Trigonometry Fall 2012 Sample Quiz 2 Solution
In Problem 4, you must show your method to receive credit.
1. [2 points] Use a calculator to nd the cosine of 3.7 . Round your answer to three
decimal places.
The value is cos(3.7 ) 0.998.
2. [2 points] Use a
Trigonometry Fall 2012 Sample Quiz 3
Two buildings stand in sight of one another. Viewed from the edge of the roof of the shorter building, the
angle of elevation of the roof of the taller building is 10 and the angle of depression of the base of the tall
Math 1613, L. Brown
Section 1.3: Trigonometric Ratios and Right Triangles
Pythagorean Theorem
In any right triangle with legs of lengths a and b, and with hypotenuse of length c,
then a2 + b2 = c2.
Legs
Hypotenuse
c
a
Important note:
The Pythagorean
theor
Math 1613, L. Brown
Section 1.2: Similar Triangles
Similar Triangles
Two triangles are similar if their corresponding angles have the same measure. Since
the angle sum for a triangle is 180, then if two angles in one triangle are congruent to
two angles i
Math 1613, L. Brown
Section 1.1: Angles, Degrees, Arcs
Angles
A positive angle has a
counterclockwise rotation.
A negative angle has a clockwise
rotation.
terminal
side
positive
angle
initial side
negative
angle
terminal
side
initial side
This angle can b
Trigonometry Fall 2012 Sample Quiz 5 Solution
This quiz concerns the function displayed in the following graph.
1
4
3
2
1
1
2
3
4
1
2
3
1. [2 points] What is the vertical shift of this function?
The vertical shift is 1.5. The center line is shown as a das
Trigonometry Fall 2012 Sample Quiz 7
1. Exactly one of the following equations is not an identity. Which one is it? How do
you know?
()
tan() =
sin()
cos()
()
cos() +
()
tan()
= sin()
sec()
()
cos2 () = 1 + sin() sin()
1 2
sin () = 1
2
2. Express
sin() ta
Trigonometry Fall 2012 Sample Exam 2 Solution
There are eight problems. With the exception of Problems 1 and 3(a), you must show your method to
receive credit.
1. [5 points] Consider the sine/cosine wave shown in the following diagram. No scales are shown
Trigonometry Fall 2012 Sample Exam 2
There are eight problems. With the exception of Problems 1 and 3(a), you must show
your method to receive credit.
1. [5 points] Consider the sine/cosine wave shown in the following diagram. No scales are
shown on the a
Trigonometry Fall 2012 Sample Exam 1 Solution
There are nine problems. With the exception of Problems 1 and 6, you must show your
method to receive credit. Even in those problems, it is safer to add some explanation.
1. Use a calculator to evaluate each o
Trigonometry Fall 2012 Sample Exam 3 Solution
1. [10 points] Use a calculator to evaluate cos1 (0.95). Answer in degrees and round your answer to
two decimal places.
cos1 (0.95) 161.81
2. Let x 1.
(a) [3 points] Simplify cos cos1 (1/x) .
(b) [4 points] Si
Trigonometry Fall 2012 Sample Final Exam Solution
1. [2 points each] Use a calculator to evaluate each of the following. Round your answers to three decimal
places.
(a) tan(1)
tan(1) 1.557
(b) csc(27.8 )
csc(27.8 ) =
1
sin(27.8 )
2.144
(c) sin1 (0.624)
s
Trigonometry Fall 2012 Sample Exam 1
There are nine problems. With the exception of Problems 1 and 6, you must show your
method to receive credit. Even in those problems, it is safer to add some explanation.
1. Use a calculator to evaluate each of the fol
Trigonometry Fall 2012 Sample Quiz 3 Solution
Two buildings stand in sight of one another. Viewed from the edge of the roof of the shorter building, the
angle of elevation of the roof of the taller building is 10 and the angle of depression of the base of