Find the values of the six trigonometric functions for
Warm-Up: February 9, 2016
Homework Questions?
Trigonometric Functions of Any
AngleSection 4.4
We are no longer restricting ourselves to points on the unit circle.
Points can now be any distance “” away from the origin
Points are still always on the terminal side of θ. Initial side is still the positive -axis.
What’s New?
22 yxr
Name Abbreviation Relation to (x, y) and r
Restriction
Sine sin y/rCosine cos x/rTangent tan y/x x≠0Cosecant csc r/y y≠0Secant sec r/x x≠0Cotangent
cot x/y y≠0
The Six Trigonometric Functions
Let be a point on the terminal side of . Find each of the six trigonometric functions of .
Example 1
Let be a point on the terminal side of . Find each of the six trigonometric functions of .
You-Try #1
All Students Take Calculus
AS
T C
a) If and , in which quadrant does lie?b) If and , in which quadrant does lie?c) If and , in which quadrant does lie?
You-Try #3
Given that and , find the value of the rest of the trigonometric functions
Example 4
Given that and , find the value of the rest of the trigonometric functions
You-Try #4
Read Section 4.4 Page 474 #1-33 odd
Assignment
Given that and , find the value of the rest of the trigonometric functions
Warm-Up: February 10/11, 2016
Sections 4.1, 4.2, 4.4, and cofunctions from 4.3
20 questions◦ 8 multiple choice◦ 2 multiple response◦ 10 free response
No calculator You will get a blank unit circle with the test
◦ Filling it out is optional
Chapter 4A Test
Mr. Szwast is available most days during lunch in room 454 and after school in room 410.
Student tutors are available Mondays through Thursdays after school in room 410.
Edgenuity – you can sign up now for Chapter 4 A. Can be used to bring your test grade up to 70%.
www.khanacademy.org – instructional videos Interactmath.com – extra practice problems
aligned to our textbook
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Homework Questions?
We like dealing with acute angles . We can often find trig functions of non-acute
angles by using an acute reference angle. Let be a non-acute angle in standard position
that lies in a quadrant (not on an axis) Its reference angle is the positive acute
angle formed by the terminal side of and the -axis
Reference Angles
For
Quadrant I:
Quadrant II:
Quadrant III:
Quadrant IV:
Finding the Reference Angle
360'180'
180''
Find the reference angle θ’ for each of the following angles:
You-Try #5
6)67)
120)160)
d
c
ba
1) Find the associated reference angle, 2) Find the trig function value of 3) Use the quadrant which lies in to choose
the appropriate sign to the value found in step 2
Using Reference Angles to Evaluate Trigonometric Functions
Find the exact value of each of the following:
Example 6
617sec)
225sin)240csc)47tan)
d
cb
a
Find the exact value of each of the following:
You-Try #6
4cot)
120tan)135cos)65sin)
d
cb
a
Trig Values Table
Read Section 4.4 Page 474 #1-33 odd Page 474 #35-65 Odd No calculators!
Assignment