Download Topic Assigned Work Done Prerequisite Skills Pg 4-5 #1

Topic
Prerequisite Skills
1.1 Revisit the Primary Trig Ratios
1.2 Solve Problems Using Trig Ratios
1.3 The Sine Law
1.4 The Cosine Law
1.5 Make Decisions Using Trig
Review
Test
Assigned Work
Pg 4-5 #1-10
Pg 13-15 #1-12
Pg 21-23 #1-6, 8, 11-15
Pg 31-33 #1-3, 5, 8, 9
Try 13!!
Pg 39-41 #1-5, 7-10, one of 11-13
Pg 48-51 #1, 2abc, 3, 4, 6-8, 10,
11, one of 12-14
Pg 52-53 #1-9, 12-17
Pg 54-55 #1-9
Pg 58-59 #1-5, 7-10
Done
Learning Goals: By the end of this unit, students will be able to solve right-angled and
acute triangles using appropriate trigonometric strategies. Students will be able to
extend this knowledge to solve real-life application problems.
Prerequisite Skills
Example 1. Solving Equations with Squared Variables
X2 - 27 = 9
x2 + 52 = 72
How to Label Triangles
Example 2. The Pythagorean Theorem
A
A
10 m
7 cm
C
c
C
B
14 m
a
5 cm
B
Example 3. Ratios and Proportions
a) Express in lowest terms
5:10
8: 18
b) Solve for the unknown
x:5 = 4:20
3:10 = 60:y
Hint for lowest terms: any number where the last digit is even can be divided by 2 AND any number where the
last digit is 5 or 0, can be divided by 5!
Example 4. Rounding
a) Round to the nearest unit
10.4
150.78
5.589
b) Round to the nearest tenth
12.384
4.65
5.993
Example 5. Angle Sum of a Triangle
The sum of the angles within a triangle is always _________.
Determine the measure of the missing angles.
Homework
Pg 4-5 #1-10
1.1 Revisit the Primary Trigonometric Ratios
What we know:
-if we are given two sides of a right-angled triangle, we can find the length of the unknown side
using Pythagorean theorem
Do we remember?
In grade 10, you learned that you can find sides and angles of a right-angled triangle if you were
given either two sides OR 1 side and 1 angle. You used:
SOH CAH TOA
Θ  called “theta” – represents the angle
The hypotenuse is always opposite the right angle (and is the longest side!), but the
opposite and adjacent sides are identified from the reference angle.
Θ
Θ
Homework
Pg 13-15 #1-12
1.2 Solving Problems with SOH CAH TOA
1. Write the 3 equations for SOH CAH TOA
2. Describe how you know when to use SOH CAH TOA . . .
3. What are the steps for SOH CAH TOA?
1. Label sides HYP, OPP, ADJ
2. Decide SOH CAH or TOA (circle what you need & what you
have -> these sides need to be in the one you pick!)
3. Write the equation and solve for the unknown (you can write
it over 1 and use cross multiply and divide)
4. Need to find an angle? use sin-1, cos-1, tan-1
check that you can do it: □ 4. Complete “Warm UP” handout.
Let’s try an example of when we can use this trigonometry in real life . . . (see text pg. 18)
We will answer this
question on back –
start by drawing a
picture!!
4. What is an “angle of depression”??
7. What is an angle of inclination??
Homework
Pg 21-23 #1-6, 8, 11-15
1.3 Non-Right Angle Triangles – Sine Law
Have texts open to page 31 (your homework is on the back of this sheet)
Your Turn! Do Q #1, pg. 31 and check your answer in the back of the book. Help someone else if you get it right!
Your Turn! Do Q #2, pg. 31 and check your answer in the back of the book. Help someone else if you get it right!
Homework
Pg 31-33 #1-3, 5, 8, 9 Try 13!!
1.4 The Cosine Law
You can also solve a triangle if you know the following:
- Find a side: given the other two sides and their contained angle
- Find angle: given the three sides
Homework
Pg 39-41 #1-5, 7-10, one of 11-13
1.5 Making Decisions Using Trigonometry
Like always, when it comes to problem solving you need to fully read the problem, highlight key
information, and draw a diagram to help you decide what method you will use to solve it. You can use
the flow chart below to help you decide.
Trigonometry
Problem
Right-angled
Triangle
Acute
Triangle
Sine
Law
Pythagorean
Theorem
Given 2 angles and
a side
sin
cos
Cosine
Law
Given 2 sides and a
contained angle
tan
Given 2 sides and
an angle opposite
one of them
Given 3 sides
Homework
Pg 48-51 #1, 2abc, 3, 4, 6-8, 10, 11, one of 12-14
Unit Review
Review
Pg 52-53 #1-9, 12-17
Pg 54-55 #1-9
Unit Test
Homework after unit test (prep for unit 2!)
Pg 58-59 #1-5, 7-10