Rise and Sine

5 Tips for Graphing Sine and Cosine

Maybe this is the first year you are teaching graphing sine and cosine functions. Maybe you’ve taught it before and you’re looking for some ways to make it better! Or perhaps you are looking for material to supplement with your struggling learners.

Whatever brought you here, welcome! Below are some tried and true ways to teach graphing sine and cosine.

I hope you find what you are searching for, or stumble upon some idea you never knew you always needed!

Discover the Sine and Cosine Curves

Provide a way for your students to discover the curve on their own, using the unit circle:

  1. Start with finding the values of sine (or cosine) on the unit circle. Provide a table to keep track of the answers.
  2. Have students convert the fractions into decimal form.
  3. Set them loose plotting points!

After allowing some time to graph the points, this is a good time to talk about all the characteristics of the sine (or cosine) curve. Maximums, minimums, key points, amplitude, period, phase shift, vertical shift, all the things!

There are some fun ways to spice up this activity, like using uncooked spaghetti!

Depending on the vibe of the class I usually found this worksheet the best use of time and highly effective.

worksheet that guides students to graph the sine function and includes examples of transformations to the sine curve

Teach One Transformation Per Lesson

What’s the rush?

Sure amplitude can be easy enough for students to grasp, but what happens when you get to phase shift?

Set the pace slow and steady, your students will appreciate it later on!

Think of it as a marathon, not a sprint. Once you cover all the transformations for sine, then you can pick up the pace when teaching cosine.

Check out pre-made guided notes (and classwork and homework!) here.

graphing the amplitude and period of the sine and cosine functions guided notes

Provide a Neat Place for Graphing Sine and Cosine

First of all, drawing axes for each question is incredibly time-consuming!

Even if you are assigning problems from a textbook, be sure to provide a worksheet with a coordinate plane to keep students work neat and organized.

If you use a consistent format throughout the unit, then when it comes to testing time students will be comfortable and grading will be SO MUCH easier!

You can grab a freebie coordinate plane worksheet 👇🏼

Or pick up these trigonometry coordinate plane clip art files to customize your own.

Pro tip: double-check the solution fits in the coordinate you provide. Don’t want that amplitude to fly off the grid, or the period to smush the curve so you can’t read it!


Keep New Vocabulary Clear and Accessible

There are a few ways to organize vocabulary. Notes are the obvious choice.

However, it’s not always convenient to have to shuffle through backpacks to find a quick definition.

So for that reason, I also recommend placing visuals around the classroom!

Plus, I like to emphasize not all students will retain information presented orally. They may not even recall writing that particular definition down.

Having a visual they can refer to accommodate their learning style and we like when all students have the opportunity to perform well in math.

Be patient with new vocabulary! Graphing sine and cosine functions is a brand new concept to students, and we want to make sure the vocabulary is there for them to ask any questions thoughtfully!



Consider Gaps in Past Knowledge

Finding period and phase shift will result in fractions (fan favorite, amirite?) and sometimes dividing fractions.

Amplitude will require using absolute value.

Spend a bit of time reviewing these concepts ahead of time!

Make self-checking digital assignments students can do for homework, or throw questions in as warm-up problems!

Whatever you decide, you’ll thank yourself later for being proactive!

It’s frustrating for students (and teachers) when algebra skills slow down mastery of higher-level concepts.

Let me know how you make this lesson easier for your students in the comments below!

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