Trigonometry Part 1
Angles
Angle Terminology
Angles
Coterminal Angles
Coterminal Angles have the same initial and terminal sides.
Angles
Example: What are some coterminal angles for
a 45 angle?
45
Angles
Expressing Angles in Radians
As we have seen before
Graphs
Func,ons and Func,on Nota,on
FUNCTION:
A func,on is a rela,onship between two variable, where
one variable (dependent variable) depends directly on
the second variable (independent variable).
Example: y = 2x2
Trigonometry
Signs of the Trigonometric Function
Trigonometric Functions
Quadrants 2, 3 and 4
So far, we have only worked in Quadrant 1. When we move into the
other quadrants, we see that the signs of our x and y values change.
This means that the signs o
MAT8100 Essen-al Mathema-cs
Graphs of Trigonometric Func-ons
Radian Measure
Angles can also be described using a measure known as radians.
The rela-onship between degrees and radians is:
Radian measure is useful becaus
Graphing Module Review
Name: _SOLUTIONS_
1) Evaluate the following functions at the specified value. [Note that = () means that we
can write either = 3 + 1 or () = 3 + 1 to mean the same thing. In this way (3) means
the same thing as evaluated when = 3.]
Graphing Module Review
Name: _
1) Evaluate the following functions at the specified value. [Note that = () means that we
can write either = 3 + 1 or () = 3 + 1 to mean the same thing. In this way (3) means
the same thing as evaluated when = 3.]
2
a) () =
Systems of Linear Equations Review
1) Solve the following 2 2 systems in three different ways: i) graphing ii) substitution and
iii) Elimination
a) 2 4 = 1 (1)
4 6 = 2 (2)
i) To graph, put in the form = +
1
1
2 4 = 1 (1) = 2 4
2
1
4 6 = 2 (2) = 3 3
Diffi
Trigonometry Module Review
Name: _
1) Complete each of the following angle conversions: (1 mark each)
a) 106.75 = _
b) 2.075 = _
c) 126.735 = _
d) 2.25 = _
e) 36.55 = _
f)
g) 152 = _
h) 67. 53 = _
4
9
= _
2) For each triangle below state the ratio
MAT8100P Systems of Equations Review
1) Solve the following 2 2 systems in three different ways: i) graphing ii) substitution and
iii) Elimination
a) 2 4 = 1 (1)
4 6 = 2 (2)
b) 2 = 3 (1)
4 2 = 2 (2)
2) Solve the following 2 2 systems of equations by using
MODULE 1 UNIT 2
ASSIGNMENT
Total marks for Assignments Module 1 Unit 2: 44 marks
Answer the following questions. Show your work and write a final statement for
each application if needed.
1) The following expression is used for changing a temperature of 3
MODULE 1 UNIT 1
ASSIGNMENT
Answer the following questions. Show your work in the space provided and write a
final statement for each application.
1) Ursulla has overdrawn her account by $45. Initially she had $130. How much
money did she withdraw from her
MODULE 1 UNIT 3
ASSIGNMENT
Answer the following questions. Show your work in the space provided and write
final statement for each application.
a
1) A wire that is 66 metres long has to be cut into two pieces. The ratio of the
lensths of the two pieces is
MODULE 2 UNIT 3
ASSIGNMENT
Total marks for Assignment Unit 3
27 marks
Answer the following questions. Show your work.
1.
Translate. Each question is worth 2 marks.
a. the sum of one third of the number of computers c and the number of desks
d
1
cd
3
b. on
The Fundamental Theorem of Calculus is based on this limit:
f ( x) lim f ( x d ) f ( x)
d
d 0
Recall the following limits:
LAST DAY: we looked at :
f(x+d) f(x) = ( 2x
HENCE: f ( x)
=
2
4 xd 2d 2 1 )
lim
d 0
d ( 4 x 2d )
lim
d 0
d
=
f(x) =
- ( 2x
2
MATH 8201 Introduction to limits
CONCEPT OF LIMITS (algebraically)
Given f(x) = 3x + 1, find lim f ( x)
x0
Remember the f(x) = 3x + 1 is a straight line (slope of 3 and y-i tercept of 1 fro
general form of a line y = mx + b)
1)
Find the value(s) of : f(0)
MAT8201 Test 1 Review
_
Name: SOLUTIONS
1) Find the following limits:
x 216
lim
a) x 4 x4
lim
x4
b) lim
x 3
( x4 ) ( x + 4 )
x4
lim
x 3
lim x +4
x 2x6
x 3
( x3 ) ( x+2 )
x 3
lim x +2
x4
x 3
4 +4
3+2
8
5
2) Find the derivative from first principles (
Assignment 2 MAT8001
_X5
NAME:_
44
Section (
)
2
1) Evaluate the function f ( x )=2 x 4 x +7 for the following values of x . (1
mark each)
a) f (0.5 )=
b) f ( 2 )=
2) For each line below identify the slope m and the y-intercept b , and then
plot each stra
Decimals to Fractions 2
_
NAME:_
16
1) Convert the following terminating to decimals by first writing the decimal number as a
fraction over a power of 10, and then simplify/reduce the fraction to simplest form.
a) 0.4
b) 0.48
c) 1.25
d) 8.785
e) 9.4375
f)
Review- chapter
4
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
1) -106'
A)254";-286"
B)74";