6.3 cont. 3rd april 2013
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6.3 trignotes (1).notebook
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April 03, 2013
May 148:58 AM
More examples:
6.3 trignotes (1).notebook
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In Grade 11, we learned cosine (x) , sine (y), and tangent valuesfor 30°, 45°, 60°, and 90° positions around the unit circle.
We now switch these positions to radian measure. These angles needto be memorized. (i.e: You need to know that 150° is without using the conversion formula)
Often written
Notice that the tangentvalues are not includedon this diagram but needto be learned as well!
6.3 trignotes (1).notebook
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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)
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More Practice:
1.
In question b) since we do NOT know exact values for thedenominator 7, we use our calculator. How will we doCosecant?
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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)
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May 149:19 AM
Use your calculator to help with these:
a) Find from for
b) Find from for
c)
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May 149:43 AM
Now: given point locations, find trig ratios and then findangle 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
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If find :
a)the values for the other 5 trigonometric ratios.
b) find the possible values of if the domain is
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May 141:14 PM
Now try these:
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May 141:15 PM
Now try these:
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May 141:17 PM
The final topic involves the ARC length around the outside of a circle (denoted as "s")
r s
Remember from the beginningof this lesson that if s=r, then anglehas the measure 1 radian.Therefore if s=10cm and r=5cmwhat 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!
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May 141:40 PM
Example Questions:
1) If a wheel of radius 40cm rolls 3m, whatis the angle of rotation in DEGREES?
2) A ferris wheel of radius 40m, rotates through an angle of 200°. What is the arc length ofthis rotation?
3) 2 cities are at the same longitude. City A is 29°Nwhile city B is at 43°S. If the earth has a diameterof approximately 12 800 kms, find the distancebetween the 2 cities.
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HOMEWORK:Page494 #4,5,6,7,8
9a),11,12,1414 Mult. Ch. #1,2BONUS: #10