Download cos(different angle)

2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
February 14, 2017
8
46 #2
answer on next page
1)
21 3
=
28 4
2)
16 8
=
34 17
3)
28 4
=
35 5
4)
32 4
=
24 3
5)
30 13
=
34 17
6)
32 8
=
40 5
7)
24 3
=
40 5
8)
14 7
=
50 25
9)
24 4
=
30 5
10)
27 3
=
36 4
p 44 #1­10
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
February 14, 2017
p 46 #2
but if sine is opp/hyp and tangent is opp/adj, how are the numerators different?
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
February 14, 2017
p 47
Look at this chart. It has the sine, cosine, and tangent values for every integer angle between 0 and 90
4
Look at: sin 15 and cos 75
sin 30 and cos 60
sin 45 and cos 45
What do you notice?
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
3
February 14, 2017
Sometimes the sine and cosine have the exact same value. In fact, if you read down the sine values it will be the same as reading up the cosine values.
What is true of the angle measures when the sine value is the same as the cosine value?
They add up to 90 o 2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
February 14, 2017
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
10
February 14, 2017
p 48­49
alpha and beta­ other Greek letters
Which makes them what kind of angles?
To generalize this: (you should write this)
When the sine and cosine of two angles have the same value, it means that those angles are in the same triangle. This means the angles are complementary (that they add to 90)
Goal 7
The sides of the triangle are the same, only the labeling changes (depending on where we are).
This is why it is important to know the sides and know the ratios and why we spent a day on each.
Also...
This is why we call some cofunctions. (co ­ sine)
They are related by complimentary angles
complementary
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
5
February 14, 2017
p 49
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
if need more practice
Complete the statement
sin 38 = cos ____
sin ___ = cos 21
sin (x+2) = cos 34
February 14, 2017
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
2
Assignment: 53­56 all
Exit question
February 14, 2017
p 55 has some more explanation as well
complete this statement
sin 78 = cos ______
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
25 minute lesson
February 14, 2017
What does Dx, 4 mean?
What does cos mean?
P 171
1a) 26
b) 60
c)17.5
d) 60 2) equal , 1/2 + (root3)/2
p 172 1a) 58
b) 35
1) they are complimentary (add to 90)
p 174
2) 0 and 90­0 represent the two angles of a triangle. Since we move our reference angle, the opposite side would then be labeled as the adjacent (sine ­­> cosine )
3a) 48 b) 78
4a) 60 b) 37
c) 45
c) 45
d) 90
d) 90
e) 25
e) 20.33
f) 11.5
f) 36
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
February 14, 2017
Extending the connection to the future
What does Dx, 4 mean?
but dilate what?
We need to know the figure to dilate. A dilation is a function. We need the input
Likewise, it is not appropriate to just have cos (or as some of you did cos =12)
Cosine is the function that says take the adjacent side and divide it by the hypotenuse.
But adjacent to what?
You need the angle.
Whether it be an angle name (cos A)
a variable expression
(cos x)
or a numeric value
(cos 12)
We need to tell what angle we are referring to (the input of the function)
Trig Functions
Input is an angle
Output is a ratio of sides
2C ­ Lesson 27 ­ Cofunctions and Special angles.notebook
February 14, 2017
go over Dr. Evil problem
exit
30
6
7
x
Which is bigger, x or 30?
Why?