Download 01 trigonometric ratios of any angle in standard position.notebook

01 trigonometric ratios of any angle in standard position.notebook
page 466 - 6.1 Trigonometric Ratios for Any Angle in Standard Position
November 12, 2012
Special Triangles and Exact Values for the Trigonometric Ratios
30o - 60o - 90o Triangles
Special Triangles and Exact Values for the Trigonometric Ratios
45o - 45o - 90o Triangles
1
30
2
2
2
1
60
2
1
1
1
1
= 45o
1
Nov 7­1:21 PM
Nov 8­8:06 AM
Determine the exact coordinates of
P , Q , R and S.
Q
Angles in Standard Position
• find the initial arm
• find the terminal arm
• rotate the terminal arm
counterclockwise
• mark 90, 180, 270 and 360
degrees
y
4
3
R
2
S
1
x
­4
­3
­2
­1
0
1
2
3
4
­1
­2
­3
•
•
•
•
­4
Nov 8­8:13 AM
Example 1
•
•
•
•
approximate and mark 45 deg
135 deg
225 deg
315 deg
approximate 130 deg
560 deg
-130 deg
-560 deg
Nov 8­8:16 AM
The Unit Circle and CAST
a) Determine 3 positive angles co-terminal with 150o
the primary ratios
the reciprocal ratios
b) Determine 3 negative anglesco-terminal with 150o
c) Give a general expression for all angles co-terminal
with 150o
Nov 8­8:25 AM
Nov 8­8:33 AM
1
01 trigonometric ratios of any angle in standard position.notebook
Draw 135o and state the reference angle.
Use special triangles and CAST to determine all 6 trigonometric ratios of 135o
Draw -225o and state the reference angle.
Use special triangles and CAST to determine all 6 trigonometric ratios of -225o
Nov 8­8:49 AM
Draw 330o and state the reference angle.
Use special triangles and CAST to determine all 6 trigonometric ratios of 330o
November 12, 2012
Nov 8­8:51 AM
Draw -240o and state the reference angle.
Use special triangles and CAST to determine all 6 trigonometric ratios of -240o
Nov 8­8:52 AM
Nov 8­8:52 AM
Example 2
Draw 156o and state the reference angle.
a) Use special triangles and CAST to determine all 6 trigonometric ratios of 510o
Use the calculator to approximate all 6 trigonometric ratios of 156o
Nov 8­8:54 AM
Nov 8­8:47 AM
2
01 trigonometric ratios of any angle in standard position.notebook
November 12, 2012
b) Use the calculator to approximate all 6 trigonometric ratios of -416o
Circles of radius r and CAST
the secondary ratios
the primary ratios
Nov 8­8:53 AM
Example 3
Determine the exact values of all 6 ratios. Then
determine the angle to the nearest tenth of a
degree. What reference angle did you use?
Nov 8­9:20 AM
Determine the exact values of all 6 ratios. Then determine the angle to the
nearest tenth of a degree. What reference angle did you use?
(-8,-5)
Nov 8­9:24 AM
Nov 8­9:26 AM
Determine the exact values of all 6 ratios. Then determine the angle to the
nearest tenth of a degree. What reference angle did you use?
What reference angle did you use?
(3,-10)
Nov 8­9:28 AM
Nov 8­10:08 AM
3
01 trigonometric ratios of any angle in standard position.notebook
What reference angle did you use?
November 12, 2012
What reference angle did you use?
Nov 8­10:14 AM
Nov 8­10:15 AM
Example 4
Example 4
Nov 8­9:54 AM
Nov 8­10:06 AM
like #3 page 474
Evaluate sec(-186o) in two ways.
Nov 8­10:07 AM
Nov 8­10:32 AM
4
01 trigonometric ratios of any angle in standard position.notebook
November 12, 2012
like #5 page 475
like #4 page 474
Sketch 620o in standard position and identify the reference angle
b) State the general formula for all angles co-terminal to the given angle.
Nov 8­10:37 AM
like #6 page 476
Nov 8­10:38 AM
like #7 page 477
Complete this chart.
Determine the exact values for the 6 ratios for -870o
Nov 8­10:49 AM
like #8 page 477
Nov 8­10:53 AM
like #10 page 478
Determine the exact values of the ratios and find the angle to 1 decimal place. The
point at the end of the terminal arm has coordinates P(-5,-11). State the reference
angle.
Nov 8­10:55 AM
Nov 8­10:57 AM
5