1. 6.3 trignotes (1).notebook April 03, 2013
More examples:
May 14­8:58 AM
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2. 6.3 trignotes (1).notebook April 03, 2013
In Grade 11, we learned cosine (x) , sine (y), and tangent values
for 30°, 45°, 60°, and 90° positions around the unit circle.
We now switch these positions to radian measure. These angles need
to be memorized. (i.e: You need to know that 150° is without
using the conversion formula)
Often written
Notice that the tangent
values are not included
on this diagram but need
to be learned as well!
May 14­8:58 AM
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3. 6.3 trignotes (1).notebook April 03, 2013
Practice Questions:
1) What is a positive coterminal angle [0 , 2 ] of:
a)
b)
2) What is the sine value of:
a)
b)
3) What is the cosine value of:
a)
b)
4) What is the tangent value of:
a)
b)
May 14­9:03 AM
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4. 6.3 trignotes (1).notebook April 03, 2013
More Practice:
1.
In question b) since we do NOT know exact values for the
denominator 7, we use our calculator. How will we do
Cosecant?
May 14­9:17 AM
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5. 6.3 trignotes (1).notebook April 03, 2013
Now let's practice the reverse concept where we FIND the angle,
GIVEN the ratio:
Find from [0,2 ] in each of the following given that:
a)
b)
c)
d)
Find from in each of the following:
e)
f)
May 14­9:18 AM
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6. 6.3 trignotes (1).notebook April 03, 2013
Use your calculator to help with these:
a) Find from for
b) Find from for
c)
May 14­9:19 AM
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7. 6.3 trignotes (1).notebook April 03, 2013
Now: given point locations, find trig ratios and then find
angle values, in radians.
1) Using P(1,2) find:
a)
b) find from
2) Using P(2,­3) find:
a) find and
b) find from
c) find from
May 14­9:43 AM
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8. 6.3 trignotes (1).notebook April 03, 2013
If find :
a)the values for the other 5 trigonometric ratios.
b) find the possible values of if the domain is
May 14­2:05 PM
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9. 6.3 trignotes (1).notebook April 03, 2013
Now try these:
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10. 6.3 trignotes (1).notebook April 03, 2013
Now try these:
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11. 6.3 trignotes (1).notebook April 03, 2013
The final topic involves the ARC length around the outside
of a circle (denoted as "s")
r s
Remember from the beginning
of this lesson that if s=r, then angle
has the measure 1 radian.
Therefore if s=10cm and r=5cm
what would be the angle size?
,,,if s=20cm and r=5 then =____
We arrive at the following ratio:
This ratio is called the Arc Length ratio and is often denoted
This ratio requires the angle to be in RADIANS!
May 14­1:17 PM
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12. 6.3 trignotes (1).notebook April 03, 2013
Example Questions:
1) If a wheel of radius 40cm rolls 3m, what
is the angle of rotation in DEGREES?
2) A ferris wheel of radius 40m, rotates through
an angle of 200°. What is the arc length of
this rotation?
3) 2 cities are at the same longitude. City A is 29°N
while city B is at 43°S. If the earth has a diameter
of approximately 12 800 kms, find the distance
between the 2 cities.
May 14­1:40 PM
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13. 6.3 trignotes (1).notebook April 03, 2013
HOMEWORK:
Page494 #4,5,6,7,8
9a),11,12,14
14 Mult. Ch. #1,2
BONUS: #10
May 14­1:52 PM
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