April 26, 2013
Warm Ups 12-5 Alg 2
1. Let (-3,7) be a point on the terminal side of
the 6 trig functions of .
2. What is the sin, cos, and tan of
?
Find reference angles for the following:
a. 192o
b. -55o
c.
. Evalutate
April 26, 2013
questions on #12-2 p. 788?
questions on #12-3 p. 783?
April 26, 2013
April 26, 2013
April 26, 2013
Signs of Function Values
sin x
cos x
tan x
sin x
cos x
tan x
sin x
cos x
tan x
sin x
cos x
tan x
evaluate without a calculator:
1. cos
2. sin
3. tan -120o
April 26, 2013
UNIT CIRCLE
is a circle with radius 1
(0,1)
(1,0)
(-1,0)
(0,-1)
Imagine wrapping the real number line around this circle, with
positive numbers corresponding to a counterclockwise wrapping.
Each number t will correspond to a point (x,y) on the circle.
What point on the circle represents t = 0?
' ' ' ' ''' '' ' '' '' ' t=2 ?
' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 't = ?
' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 't = /2 ?
April 26, 2013
Each number t also corresponds to a central angle whose
radian measure is t.
recall arc length s = r
with r = 1
which indicates that t is the length of the arc subtended
(0,1)
by
place the
following arcs
on the unit
circle which
correspond to
the radian
angles:
(-1,0)
0
(0,-1)
(1,0)
April 26, 2013
Put the radian angles in degrees also.
(0,1)
(-1,0)
0
(0,-1)
(1,0)
April 26, 2013
Find the coordinates of the points on the circle using special
triangles.
(0,1)
o
120o 90
135o
60o
45o
30o
150o
(-1,0)
0
180o
0o or 360o
330o
210o
225o
240o
315o
270o
300o
(0,-1)
(1,0)
April 26, 2013
(0,1)
o
120o 90
135o
60o
45o
30o
150o
(-1,0)
0
180o
0o or 360o
330o
210o
225o
240o
315o
270o
300o
(0,-1)
(1,0)
April 26, 2013
These problems just got easier!
(0,1)
Find exactly.
135o
1. cos 315o
o
120o 90
60o
45o
30o
150o
(-1,0)
2. sec
0
180o
0o or 360o
225o
3. tan 210o
330o
210o
240
315o
o
270o
300o
(0,-1)
(1,0)
April 26, 2013
The horizontal distance d (in feet) traveled by a projectile
with an initial speed v (in feet per second) is given by
d = v2/32 sin 2
where
is the angle at which the projectile is launched.
Find the distance traveled by a golf ball that is hit at an
angle of 50o with an initial speed of 105 feet per second.
April 26, 2013
#12-5
p. 788 6-21
70, 71, 73, 74, 90, 91