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P.o.D. – Use the unit circle to find each of the following.
1.) sine of 330 degrees
2.) cosine of 150 degrees
3.) sine of -120 degrees
4.) cosine of -315 degrees
5.) sine of 210 degrees
6.) sine of 180 degrees
7.) cosine of -270 degrees
10-5: Relationships among Sines and Cosines
Learning Target: I can identify and use the definitions of sine,
cosine, and tangent; identify and use theorems relating sines and
cosines; use the properties of a unit circle to find trigonometric
ratios.
Let’s Review:
The Cartesian Coordinate System
Quadrant __
Quadrant __
Type equation here.
Quadrant ___
Think back to the Unit Circle
Quadrant __
Cosine = _________________
Sine = ______________
Tangent =
Sin,Cos,Tan by Quadrant:
Q2:
QI:
Q3:
Q4:
A
S
T
C_____________
Basic Pythagorean Identity:
EX: Suppose that an angle of 52 degrees in standard position
intersects the unit circle. (Draw a picture on the whiteboard).
a.)
Approximate the coordinates of point C.
b.)
Verify that your coordinates in part (a) satisfy the
Pythagorean Identity.
EX: Show that cos 252° = − cos 72°
EX: Find an exact value for the sine of 330 degrees. (Draw the
unit circle on the whiteboard).
We need to recognize that ________ degrees also creates a ___
degree angle.
In other words, , ______________________________________
These should be memorized values.
Values that you must have memorized:
30°
45°
60°
Sine
Cosine
tangent
EX: Use the unit circle to find the value of each of the following:
a.)
b.)
c.)
Cosine of 90 degrees
Tangent of 270 degrees
Sine of (-90) degrees
EX: Use the unit circle to find the sine, cosine, and tangent of each
of the following:
a.)
b.)
45 degrees
120 degrees
EX: Find the sine, cosine, and tangent for the given angle in
standard position if the given point lies on its terminal side.
a.)
b.)
c.)
(-1,5)
(7,6)
(-3,-4)
(Draw each point on the whiteboard) – notice that we are no
longer on ______________________________.
EX: Consider a right triangle with C as the right angle. If A=55.56
degrees and side c=16, find side a. (Draw a picture on the
whiteboard).
EX: Using the same right triangle as previously described, find
side b if side a=9 and angle B=49 degrees.
EX: Given triangle ABC with C as the right angle, find the
following on your own.
a.)
b.)
c.)
If B=56.48 degrees and c=63.1, find b.
If B=64degrees and b=19.2, find a.
If b=14 and A=16degrees, find c.
EX: A 30-ft ladder leaning against the side of a building makes a
70.5 degree angle with the ground. (Draw a picture on the
whiteboard).
a.)
How far up the side of the house does the ladder reach?
b.)
What is the horizontal distance between the bottom of
the ladder and the house?
HW Pg.690
1-20, 22, 24
Quiz 10.1-10.5 tomorrow