1. Module 7

1.35. Page 2

Mathematics 10-3 Module 7 Lesson 7

Module 7: Trigonometry

 

Get Started

 

In this activity you will investigate memory aids to remember the definitions of sine, cosine, and tangent.

 

m10_3_trythis.jpg Try This

 

Work with a partner, if possible.

 

Look at the following diagram.

 

 

This illustration shows right triangle ABC with angle C as the right angle. BC, a vertical side, is coloured orange and is labelled side opposite. AC is horizontal and is coloured green. AB is black and is labelled hypotenuse. Angle A is filled with red.

 

Do you remember how the sides of the right triangle are identified in relation to ∠A? What are the definitions for sin A, cos A, and tan A?

 

 

 

The first letters from the definitions spell SOH-CAH-TOA. This word is pronounced Soak a Toe! Ahhh.

 

For some people, just the word SOH-CAH-TOA is enough to help them remember the trig ratios. Others find that attaching words to each letter of SOH-CAH-TOA helps them remember. No one method is best. You must find a method that works for you!

 

TT1. Randy remembers SOH-CAH-TOA this way.

 

 

SOH Saskatoon Our Home (Randy lives in Saskatoon.)

 

CAH Calgary Alberta Hockey (The Calgary Flames are Randy’s favourite team.)

 

TOA Toronto Ontario Aunt (Randy’s favourite aunt lives in Toronto.)

 

Randy’s choices aren’t the choices you will make, but use Randy’s method to pick words you will easily remember.

 

TT2. Jenn uses the first letter of each word in the following sentence to remember SOH-CAH-TOA.

 

 

Sweep Over Here, Cathy, Aunt Hazel’s Tossing Oatmeal Again!

 

Make a sentence you will easily remember.

 

Share

 

Share the memory aids you created for TT 1 and TT 2 with a partner or with a group. Explore some of the memory aids created by others. Which of these memory aids will help you most?

 

Save a copy of your favourite memory aid in your course folder.

 

Explore

 

In previous lessons, questions were grouped by trigonometric ratio. In Lessons 1 and 2, you examined the tangent ratio and its applications. Then in Lessons 3 and 4, you studied the sine ratio. And in Lessons 5 and 6, you dealt with the cosine ratio. But suppose you are given a general problem involving one or more trigonometric ratios. How do you decide which ratio to use?

 

In this activity you will use trigonometric ratios—sine, cosine, and tangent—in a game of mini golf.

 

Try This

 

Work with a partner, if possible.

 

You will play mini golf with “Exploring Trig Ratios—Use It.” In previous lessons you used the “Explore It” features of the “Exploring Trig Ratios” interactive. This time, select “Use It.” By answering each trigonometry question correctly, you will make your way from tee to green!

 

TT 3. Which ratio do you find easiest to remember? Why? Did your memory aid from Get Started help you remember the ratios?

 

TT 4. Which do you find easier, finding angles or finding sides? Why?

 

Discuss these answers with your teacher.