Teaching Ideas for Trigonometry

Yes, that section….

Things to tackle in Trigonometry

• Pythagoras

• Reciprocals

• Ratios

• Special Angles and proving the CAST diagram

• Graphs – the effects of a, p and q

• Proving identities

Handy things to know• Drill Mode

• Press

•

•

•

•

• Answer the questions and press

• If you accidently type in something wrong press

Math DrillQuestion?25

◄ + ‒ x ÷ + ‒ x ÷ ►

SELECT & [ENTER]

Class marks• Press

• Type in what you are converting to, e.g. 100

• Press

• Type in what you are converting from, e.g. 80

• Press

• Type in first student’s mark

• Press

• Then simply type in the next student’s mark and again

100

80× 55 =

683

4

PRIME FACTORIZATION!!!!!!

• Press

• Type in the number you want to prime factorize.

• Press

•

•

• Tada!! ☺

96 =

25x3

Pythagoras

• Type in the x-coordinate

• Press

• Then type in the y-coordinate

• Press

•

4,3 → rθ

r: 5.θ: 36.86989765

You can also go backwards…

• Type in hypotenuse

• Press

• Type in angle

• Press

•

5,36.87 →xy

X: 3.999994641Y: 3.000007146

Reciprocals

• For sec x:• Press

• For cosec x:• Press

• For cot x:• Press

1

cos 30=

2 3

3

Ratios

• Save sin-1 into D1 key:

•

•

•

•

• Now press and 1 2

STORING D1

SELECT FUNCTION

Special Angles

• Or use your calculator:

• 30

• 30

• 30

• And so on…

Proving the CAST Diagram.

• Press

• Start with sin – so type in

•

•

• At X-Start, start at -90 so type in

• At X-Step, type in 15

X_Start:-90.

X_Step:15_

• Look at the y-values between• -90 and 0

• 0 and 90

• 90 and 180

• 180 and 270

• 270 and 360

• 360 and 450

• 450 and 540 and so on…

X ANS-90 -1-75 -0.9659-60 -0.8660 -90

Now let’s do cos

• Press

• Now type in

•

•

• At X-Start, start at -90 again, so press

• At X-Step, leave as 15, so

X ANS-90 0-75 0.25881-60 0.5 -90

And now tan

• Press

• Now type in

•

•

• At X-Start, start at -90 again, so press

• At X-Step, leave as 15, so

X ANS-90 ---------75 -3.7320-60 -1.7320 -90

So what have we got?

Sin(x)

Sin(x) Sin(x)

Sin(x) Sin(x)

Sin(x)Cos(x)

Cos(x)

Cos(x)

Cos(x)

Cos(x)

Cos(x)

Tan(x)

Tan(x)

Tan(x)

Tan(x)

Tan(x)

Tan(x)Notice a pattern?

Lets look at the positives:

A

C

S

T

90

180

270

0 or

360

Graphs – the effects of a, p and q:

• Basic Sin graph:• As we did when

proving the CAST diagram – plot the coordinates.

Let’s investigate a:

• Press

•

• 2

• x 3

• Plot the new coordinates.

• What happens if

a = ½?

Yes, it gets smaller:

Same idea for p = 1, 2, and ½

And q = 0, +1, -1

Proving Identities

• Prove that sin2 𝑥 + cos2 𝑥 = 1• Press

•

•

•

•

(sinX)2 + (cosX)2_

Thank you!Take a look at

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for lots of high school worksheets with memos, sample exam

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