Trig Ratios with Obtuse Angles
February 05, 2014
What's Going On?
Angles in Standard Position
Obtuse Angles in Standard Position
Writing the Ratios
Learning Goal ­ I will be able to write the trigonometric ratios of acute and obtuse angles in standard position.
Sep 12­9:36 AM
Trig Ratios with Obtuse Angles
February 05, 2014
Angles in Standard Position
y
θ
x
An angle in standard position is measured counter­clockwise about the origin from the positive x­axis on the Cartesian plane.
Sep 11­7:45 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Angles in Standard Position
y
θ
x
The primary trigonometric ratios of an angle, θ, in standard position are defined in terms of the coordinates of a point, (x, y).
Sep 11­7:45 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Angles in Standard Position
y
θ
x
Feb 4­2:13 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Angles in Standard Position
y
θ
x
Feb 4­2:17 PM
Trig Ratios with Obtuse Angles
February 05, 2014
a. sketch a diagram of the angle in standard position.
b. determine the distance from the origin to the point
c. determine the primary trig ratios for the angle
d. determine the angle
Feb 4­2:22 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Feb 4­2:26 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Angles in Standard Position
y
θ
x
The primary trigonometric ratios are defined as follows:
Sep 11­7:45 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Obtuse Angles in Standard Position
y
θ
β
x
The primary trigonometric ratios of an obtuse angle in standard are measured in the same way as an acute angle in standard position.
The only real difference is that
Sep 11­7:45 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Writing the Ratios
For each given point that lies on the terminal arm of an angle:
a. Sketch a diagram for the angle in standard position. b. Determine the distance from the origin to the point.
c. Determine the primary trigonometric ratios to four decimal places.
d. Determine the measure of the angle.
Sep 10­4:54 PM
Trig Ratios with Obtuse Angles
February 05, 2014
Writing the Ratios
y
x
Sep 10­4:54 PM