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Topic 2: Trigonometry
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Achievement Standard 91575: Apply trigonometric methods in solving problems.
This standard is an Internal worth 4 credits.
Week 9 and 10: Solving trig equations.
This work needs to be completed by Monday 11 April.
Learning Objectives
1. To understand what the inverse trig functions are and the restrictions on the domain and range.
2. To be able to interpret the angle given on your calculator when using inverse trig functions.
3. To be able to use the symmetrical properties of the trig graphs to solve simple trig equations.
4. To know the general solutions for trig equations.
5. To be able to solve more complex trig equations.
Topic
Notes
Inverse trig
functions.
We have all used the inverse trig buttons on the
calculator but what are we really finding.
𝑦 = sin−1 𝑥 means that 𝑥 = sin 𝑦
𝑦 is an angle and the table in the textbook tells us the
range of angles that we will get for each of the trig
functions.
We will need to use the symmetry of the graphs to
identify angles we may want outside of this range.
I have given you a worksheet explaining how to use
the symmetry of the graphs to identify other angles in
a given range when you already know one.
Solving simple
trig equations.
General
solutions of trig
equations
The formulas for these are given on the formula sheet.
I am also sending you out a sheet explaining where
these come from. Please read it.
Solving more
complex trig
equations.
When we are solving more complex trig equations
that may have more than 2 solutions in the 0 to 2π
range, I use the general formulas to help solve them.
Below is the link to 3 video worked examples on
YouTube. Please watch these as they will
help you to follow the worked solutions
to Worksheet 2.
Worked examples on YouTube
Use the link or the QR code.
Delta Mathematics
2nd Edition Old Book
Read pages 332 to
334
Taking note of the
table at the bottom
of page 334.
Delta Maths NCEA
Level 3 New Book
Read pages 110 to
113
Taking note of the
table in the middle of
page 113.
Worksheet 1: Using
symmetry to solve
trig equations.
Read the first page
and complete the
exercises on the
second page.
Read the examples
on page 337 and 340.
Then do…
Page 340 Ex 35.3
Also read the use of
special triangles and
giving solutions as
exact values on pages
340 to 342.
Then do…
Page 342 Ex 35.4
Read the General
Solutions sheet.
I have included a
blank copy of this
sheet so you can try
and follow how the
formulas are
obtained.
Worksheet 2: Solving
trig equations.
Solutions will be on
the web page.
Worksheet 1: Using
symmetry to solve
trig equations.
Read the first page
and complete the
exercises on the
second page.
Read pages 115 to
117
Then do…
Page 117 Ex 7.03
Also read the use of
special triangles and
giving solutions as
exact values on page
117
Then do…
Page 120 Ex 7.04
Read the General
Solutions sheet.
I have included a
blank copy of this
sheet so you can try
and follow how the
formulas are
obtained.
Worksheet 2: Solving
trig equations.
Solutions will be on
the web page.