Chapter 4
Trigonometry Day 2
(Covers a variety of topics in 4.2-4.4)
6 Notecards
Six Trig Functions
sin opposite
hypotenuse
cos adjacent
hypotenuse
tan opposite
adjacent
csc hypotenuse
opposite
These are the reciprocal functions
sec hypotenuse
adjacent
cot adjacent
opposite
Six Trig Functions (continued on next slide)
To remember your trig functions:
SOHCAHTOAAnother Trig Property you need to know:
tan sincos
Ex 1: sin = 3/5
Find the other trig functions:
cos = _______
tan = _______
csc = ________
sec = ________
cot = ________
Ex 2:
Find the other trig functions:
sin = _______
cos = _______
csc = ________
sec = ________
cot = ________
tan 3
3
Suppose I give you a point on the Unit Circle:
12
13, 5
13
Any point on a unit circle (when radius is 1) is in the form
(cos,sin)Therefore:
sin 5
13& cos
12
13
tan = ______ csc = ______ sec = ______ cot = _____
•
Basic Trig Functions
1
3
260°
30°
12
1
Degrees Radians Sin Cos tan
30
45
60
64
3
1
2
1
2
3
2
3
2
3
3
3
2
2
2
21
(1,0)
(0,1)
(-1,0)
(0,-1)
90°
180°
270°
0°/360°
Use the unit circle, with a radius of 1, to figure out your trig functions for the Quadrant angles 0,90,180,270,360
Remember:
tan sincos
And that all points on a unit circle are in the form of
cos,sin
AS
T C
When doing Trig Functions in each quadrant, some functions ( and their reciprocals) are positive and some might be negative:
Here is the phrase to remember this in the quadrants:
All Students Take Calculus
Signs (+/-) of Trig functions in QuadrantsContinued on next slide
• “A” means that in the first quadrant all the trig functions are positive: SIN, COS, TAN
• “S” means that in the second quadrant only the SIN is positive, and the COS and TAN are negative
• “T” means that in the third quadrant only the TAN is positive, and the SIN and COS are negative
• “C” means that in the fourth quadrant only the COS is positive, and the TAN and SIN are negative
Continued from previous slide
Reference Angles
You will use reference angles to help you figure out the value of trig functions
Your reference angle is the angle between the terminal side and either the 180° line or the 0°/360° line
Reference Angles
Find the reference angle for the following:
1)602)2503)300
4)56
5)23
6)5554
Even and Odd Trig Functions
Cosine and Secant are EVEN:
cos(-t) = cos (t) sec(-t) = sec (t)
Sine, Cosine, Tangent, and Cotangent are ODD:
sin(-t) = - sin(t) csc(-t) = - csc(t)
tan(-t) = - tan(t) cot(-t) = - cot(t)
For example: sin(t) = 1/5, so sin(-t) = -1/5
If cos(t) = 2/3 , then cos(π+t) = -2/3