Teaching Ideas for Trigonometry
Transcript of Teaching Ideas for Trigonometry
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Teaching Ideas for Trigonometry
Yes, that section….
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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
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Handy things to know• Drill Mode
• Press
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• Answer the questions and press
• If you accidently type in something wrong press
Math DrillQuestion?25
◄ + ‒ x ÷ + ‒ x ÷ ►
SELECT & [ENTER]
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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
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PRIME FACTORIZATION!!!!!!
• Press
• Type in the number you want to prime factorize.
• Press
•
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• Tada!! ☺
96 =
25x3
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Pythagoras
• Type in the x-coordinate
• Press
• Then type in the y-coordinate
• Press
•
4,3 → rθ
r: 5.θ: 36.86989765
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You can also go backwards…
• Type in hypotenuse
• Press
• Type in angle
• Press
•
5,36.87 →xy
X: 3.999994641Y: 3.000007146
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Reciprocals
• For sec x:• Press
• For cosec x:• Press
• For cot x:• Press
1
cos 30=
2 3
3
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Ratios
• Save sin-1 into D1 key:
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• Now press and 1 2
STORING D1
SELECT FUNCTION
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Special Angles
• Or use your calculator:
• 30
• 30
• 30
• And so on…
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Proving the CAST Diagram.
• Press
• Start with sin – so type in
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• At X-Start, start at -90 so type in
• At X-Step, type in 15
X_Start:-90.
X_Step:15_
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• 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
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Now let’s do cos
• Press
• Now type in
•
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• 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
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And now tan
• Press
• Now type in
•
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• 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
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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?
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Lets look at the positives:
A
C
S
T
90
180
270
0 or
360
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Graphs – the effects of a, p and q:
• Basic Sin graph:• As we did when
proving the CAST diagram – plot the coordinates.
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Let’s investigate a:
• Press
•
• 2
• x 3
• Plot the new coordinates.
• What happens if
a = ½?
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Yes, it gets smaller:
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Same idea for p = 1, 2, and ½
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And q = 0, +1, -1
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Proving Identities
• Prove that sin2 𝑥 + cos2 𝑥 = 1• Press
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(sinX)2 + (cosX)2_
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