Interview
Trigonometric Functions (Revision)
- Course
- Institution
Revision of Trigonometric functions done in grade 10.
[Show more]
Seller
Follow
kalebroodt
Content preview
Grade 11 Trigonometric FunctionsDocument 1: Revision of Grade 10 content
𝑦 = sin 𝑥 𝑦 = cos 𝑥 𝑦 = tan 𝑥
1. Amplitude: Half the total
distance between the minimum
and maximum values.
2. Amplitude is ALWAYS positive
𝑚𝑎𝑥𝑖𝑚𝑢𝑚−𝑚𝑖𝑛𝑖𝑚𝑢𝑚
3.
2
Amplitude changes and Vertical shifts (the role of 𝒂 and 𝒒) 4. The amplitude for a tan graph is
undefined.
In Grade 10 we studied some transformations of the 3 basic trig functions.
Our transformed functions were defined as:
𝑦 = 𝑎 sin 𝑥 + 𝑞 𝑦 = 𝑎 cos 𝑥 + 𝑞 𝑦 = 𝑎 tan 𝑥 + 𝑞
When the numerical value of 𝑎 increases (ignoring the sign), the amplitude of the sin and cos
graphs increases. The numerical value of 𝑎 determines the steepness of the tan graph.
If 𝑎 is negative, the graphs are all reflected in the 𝑥 axis.
𝑞 shifts the graphs up (𝑞 > 0) or down (𝑞 < 0).
1
, Worked Example 1: Consider the function 𝑓(𝑥) = 2𝑠𝑖𝑛𝑥 − 1
1. Sketch the graph of 𝑓 for 𝑥 ∈ [0°; 360°].
2. Write down the period and amplitude of 𝑓.
3. Write down the range of 𝑓.
Solution
Thought process:
1. Step 1: Consider the basic shape (sin, cos or tan) Step 2: Consider the stretch (a value)
Start with a basic sin graph, rough sketch 𝑎 = 2. Stretch the graph vertically up to
2 and down to -2.
Step 3: Consider the vertical shift (q value)
𝑞 = −1. The graph is shifted 1 unit down. Think of the 5 critical points (the 3 zeros, the max
and the min) moved down 1 unit each and then joined to give the new sin graph.
NOTE: You may be asked to label all
Turning points and/or ‘end’ points, so you
would label (90°; 1); (270°; −3);
(360° ; −1)
2. Period: 360°
Amplitude: 2
The range is represented by
3. Range: 0 ≤ 𝑦 ≤ −3 or 𝑦 ∈ [−3; 1] 𝑦 ∈ [𝑚𝑖𝑛; 𝑚𝑎𝑥]
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller kalebroodt. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.77. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
50843 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now