Interview
Trigonometric Functions: Changes in Period and other transformations
- Course
- Institution
This document explains how to apply shifts and period changes to trig functions as well as transformations to trig graphs.
[Show more]
Seller
Follow
kalebroodt
Content preview
Grade 11 Trigonometric FunctionsDocument 4: Combined Period and other Transformations:
Worked Example 1: Sketch the graphs of the following functions:
1. 𝑦 = 2 sin 2𝑥 − 1, 𝑥 ∈ [0°; 360°]
2. 𝑦 = cos 2(𝑥 − 15°) , 𝑥 ∈ [−120°; 150°]
3. 𝑦 = tan(3𝑥 + 30°) , 𝑥 ∈ [−25°; 50°] Note the difference here in this important example!
Hint: factorise first, but the common factor of 3 does not
go in front of ‘tan’ as it is part of the ‘angle’
Solutions:
1. 𝑦 = 2 sin 2𝑥 − 1, 𝑥 ∈ [0°; 360°]
Step 1: Consider the basic shape: 𝑦 = sin 𝑥 with an amplitude of 2
Step 2: Calculate the new period
360°
𝑘 = 2 the period of this sin graph is 2
= 180°. It is useful to divide the new period by 4:
180°
= 45°. This tells me that (before the shift down) something critical will happen every 45° for the
4
basic sin graph: “ 𝑥 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡, 𝑝𝑒𝑎𝑘, 𝑥 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡, 𝑡𝑟𝑜𝑢𝑔ℎ, 𝑥 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 “. We call this the step size.
Step 3: Consider the horizontal and vertical shifts: 𝑞 = −1 so the graph is shifted 1 unit down
NOTE: You may be asked to label all
Turning points and/or ‘end’ points, so you
Step 4: Final sketch: would label (45°; 1); (135°; −3);
(225°; 1); (315; −3); (360; −1)
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 $2.76. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
52355 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now