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Evaluating Trig Functions of Quadrantal Angles Activity: Odd One Out

Are your students struggling to evaluate trigonometric functions of quadrantal angles? This Odd One Out Activity will give them plenty of practice and highlight common errors made while trying to work these types of trig problems.


In my many years of teaching precalculus, one of the trig topics that my students struggle the most to wrap their minds around is evaluating trig functions of quadrantal angles such as sin(0).

Up to this point, I have had my precalculus students using right triangles to evaluate all of the trig functions we have encountered. With quadrantal angles, however, our right triangles no longer work!

This past school year, I created this Odd One Out activity to give them plenty of practice evaluating trigonometric functions of quadrantal angles in degrees.

Earlier in the year, I used a very similar odd one out activity structure for a trigonometry reference angles activity which I shared here on the blog.

Annoyingly, I will have to redo this activity in the future since the new AP Precalculus course does all trigonometry solely in radians instead of degrees.

Activity Instructions

This activity is provided in four separate challenges. Each challenge has the same set of instructions: “Determine which trig expression has a different value than the other expressions.”

Students must determine which trig expression is the “odd one out.”

evaluating trig functions of quadrantal angles odd one out activity laying on desk in high school math classroom

Students are provided cards with four different trig expressions involving quadrantal angles. Three of the four expressions will evaluate to the exact same value.

The activity is designed so that students work though each challenge one at a time. They must evaluate all four trig expressions to determine the “odd one out” before moving on to the next challenge.

Printing and Prepping the Activity

I printed each of the four sets of problems in this quadrantal angles activity on different colors of paper.

I used my handy dandy paper chopper to easily cut each page into fourths. I clipped the four resulting cards together with a paperclip. I did not bother printing this activity on cardstock or laminating it this time.

colored angle cards laying on top of paper chopper for odd one out activity for practicing evaluating trig functions of quadrantal angles

For my students, I chose to put each set of colored problems in one of my magnetic pockets from Charles Leonard.

evaluating trig functions of quadrantal angles activity on dry erase board in high school math classroom

These magnetic pockets have been a true classroom lifesaver this past school year.

close-up of odd one out cards in magnetic pouches on dry erase board

The entire back of the pouch is a single giant magnet, so they stick on the dry erase board without constantly sliding down.

I used one of my magnetic clips to hang the instructions above the magnetic pouches full of problems.

instructions for evaluating trig functions of quadrantal angles activity hanging on dry erase board in high school math classroom

This sort of dry erase set-up is completely optional. You could definitely just hand the stacks of problems to students/groups. I just wanted to show you how I set up the activity in my own classroom.

How I Used the Activity

Since all the problems were posted at the front of the classroom, I had each group of students send a member up to grab a stack of cards.

The four different problem sets are all independent of one another, so it didn’t matter which color of cards that students chose to start with.

They brought the stack of cards back to their table where they worked together to evaluate each trig expression in the stack. When groups had found the odd one out, they brought the stack of cards to my desk to check their answer.

If they were correct, I shuffled the group’s cards and sent them back to the front of the room to grab a different color of cards. If they were incorrect, I sent them back to their group to re-evaluate their trig expressions.

I thought this activity would take about five minutes to complete. But we actually ended up spending more like 10-12 minutes on it because it surfaced so many misconceptions that my students had.

This would make a great activity for kicking off class the day after learning about evaluating trig functions of quadrantal angles.

Quadrantal Angles Worksheet

Don’t have time to cut apart cards to make a group activity? Would you rather have this activity in an easy-to-use worksheet format? I have got you covered!

worksheet version of evaluating trig functions of quadrantal angles odd one out activity

This worksheet uses the exact same problems as the group activity shared above.

screenshot of quadrantal angles worksheet version of odd one out activity

Puzzle Solutions

I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at with information about what you teach and where you teach. I will be happy to forward an answer key to you.