1.6b day 2 evaluating trig functions greg kelly, hanford high school, richland, washingtonphoto by...
Post on 19-Jan-2016
218 Views
Preview:
TRANSCRIPT
1.6b day 2 Evaluating Trig Functions
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2008
President James A. Garfield National Historic SiteMentor, Ohio
x
y
0
2
3
2
2
First, a little review.
Answer as quickly as you can!
sec 0 1
sin 0
cos 0 1
3cot
2
0
3csc
2
1
3sec
2
undefined
x
y
0
2
3
2
2
First, a little review.
Answer as quickly as you can!
sec2
undefined
cot 0 undefined
sec 1
3sin
2
1
cos2
0
tan 0
We can find exact values for certain angles using special triangles. The first is the 45o triangle.
sin 45
cos45
tan 45 If we superimpose this triangle on a unit circle, the hypotenuse would have a length of 1, and the triangle would look like this:
1
2
1
2
1
1
45
1
12
If we let the two perpendicular sides have a length of 1, then the hypotenuse is: 2 21 1 2c
2
2
2
2
1
x
y
In calculus we frequently do not have to rationalize the denominator, so we can “cheat” and re-label the sides.
0
2
3
2
2
2
2
2
1
4
sin
cos
tan
1 2
22
1 2
22
11
1
x
y
It is not a “unit” circle any more, but these labels let us quickly evaluate the trig functions.
0
2
3
2
1
12
4
sin
cos
tan
1
2
1
2
1
sec
csc
cot
2
1
2
Move the triangle to find other values.
You are welcome to rationalize the denominator any time you like!
x
y
Notice that in this position, the x coordinate is negative.
0
2
3
2
1
12
3
4
sin
cos
tan
1
2
1
2
1
sec
csc
cot
2
1
2
x
y
Here both the x and y coordinates are negative.
0
2
3
2
1
12
5
4
sin
cos
tan
1
2
1
2
1
sec
csc
cot
2
1
2
x
y
In this position, the y coordinate is negative.
0
2
3
2
1
12
7
4
sin
cos
tan
1
2
1
2
1
sec
csc
cot
2
1
2
It is great if you can memorize these or picture the unit circle or special triangles in your mind.
However, a quick sketch and a correct answer is always better than a guess and a wrong answer!
top related