Download Analysis I 7-3 The Sine and Cosine Functions

7-3 Points Not On The Unit Circle
Points not on the Unit Circle
Cosine
x
adjacent
cos   
r hypotenuse
Sine
y
opposite
sin   
r hypotenuse
Tangent
y opposite
tan   
x adjacent
P (x, y)
r
y

x
If the terminal ray of an angle in standard
position passes through (-3, 4), find the sine,
cosine, and tangent of the angle.
Steps
1. Sketch a picture of the circle
centered at the origin that goes
through the given point
2. Create a right triangle by
dropping an altitude to the x-axis
1. The angle formed is call a
reference angle for the
originally described angle
3. Use the Pythagorean Theorem to
solve for the third side of the
triangle
4. Use SohCahToa to find each of
the trigonometric ratios for the
original angle described
P (-3, 4)
r
Where are Cosine and Sine
positive and negative?
Cosine
-
+
+
Sine
+
+
-
-
Signs of Trig. Functions on Unit
Circle
Sine
All
Tangent
Cosine
Where are the trig. functions positive?
State whether the sine and the cosine of
each angle is positive, negative, or zero.
 2
3
3
-
Complete each statement using
<, >, or =
a) sin 30˚_______sin (-30˚)
b) cos 30˚_______cos(-30˚)
c) cos 300˚______cos 330˚
#1
If the terminal ray of an angle in standard
position passes through (-3, 1), find the sine,
cosine, and tangent of the angle.
#2
If the terminal ray of an angle in standard
position passes through (1, -2), find the sine,
cosine, and tangent of the angle.
#3
If the terminal ray of an angle in standard
position passes through (-10, -8), find the
sine, cosine, and tangent of the angle.
#4
If the terminal ray of an angle in standard
position passes through (7, 5), find the sine,
cosine, and tangent of the angle.
#5
If the terminal ray of an angle in standard
position passes through (-6, -2), find the
sine, cosine, and tangent of the angle.
#6
If the terminal ray of an angle in standard
position passes through (9, -10), find the
sine, cosine, and tangent of the angle.
#7
If the terminal ray of an angle in standard
position passes through (-5, 12), find the
sine, cosine, and tangent of the angle.
If  is a third-quadrant angle and
sine is -5/13, find cos 
-5
13
Homework
• P.271: #4
• P.272: #17-20
Warm-Up