Download Section 1.4 Day #2 Notes.jnt

Trigonometry
Section 1.4 Continued
Notes
Let’s look at some identities;
Reciprocal Identities:
Given the point (-3, 4) on the terminal side of an angle in standard position, find the
six trigonometric function values in exact form.
Based on the definitions of the trigonometric functions, and looking at an example,
we know that the value of sine is the reciprocal of the value of cosecant. Which
means, if I know the value of sine, find the reciprocal and we know the value of
cosecant. We do NO WORK!
In visual form; sin 
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csc
sec 
csc 
1
sin
so…
tan 
cos 
cot 
Pythagorean Identities:
These identities stem from the definition of r, and how we can relate the definition to
the definition of the trigonometric functions.
r  x2  y 2
We can eliminate the radical by taking the square root of both sides…leaving us with;
There are THREE Pythagorean Identities; let’s find them!
Pythagorean Identity #1:
Divide all parts of the above equation by r 2 ;
Applying a nice little algebra trick;
Using the definitions;
Trigonometry
Section 1.4 Continued
Notes
Repeating the process, but dividing first by x2 and then by y2 , find the other two
Pythagorean identities.
Quotient Identities: I will just give these to you;
tan  
sin 
cos
cot  
cos
sin 
Using what we now have:
Example: Find the remaining six trig functions given;
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cos    ,  terminates in quadrant II .
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