Download MAT 1-13

MAT & Trig
Notes 1.3 Day 1
Mathematician:
OPENER
1)
Graph and label the following point on the axis provided.
Point A (-3, 5)
Point B (8, -4)
Point C (-2, - 8 )
2)
Find the missing side of each right triangle using the Pythagorean Formula.
6
8
3)
Refer to the diagram at the right, fill in the blanks.
The leg adjacent to
X
 is _________________.
The leg opposite to  is__________________.
Z
The hypotenuse is _____________________.
Y

Fill in the blank with the name of a trigonometric ratio. On the right, give the reciprocal trig ratio.
The ______________of  =
opposite side
adjacent side
The _______________of  =
adjacent side
hypotenuse
The _______________of  =
opposite side
hypotenuse
There is a shortcut to remember this:
___________________________________________________________________
NOTES
At this stage you should be very familiar with sine, cosine and tangent. There are actually 3 more trig
functions that are simply the reciprocal of sine, cosine and tangent.
If the sin  =
opposite side
hypotenuse
, then the _______________of  =
hypotenuse
opposite side
If the cos  =
adjacent side
hypotenuse
, then the _______________of  =
hypotenuse
adjacent side
If the tan  =
opposite side
adjacent side
, then the _______________of  =
adjacent side
opposite side
Ex 1:
Find the EXACT value of trigonometric function. (Exact values do not have decimals.)
Refer to the triangle on the right. Always reduce your fractions.
sin  
sec  
cos  
cot  
tan  
csc  
Today we are going to attempt to look at a picture on a graph and identify those 6 trig functions. Think
about the refresher we just went through and graph the following points.
a)
(-3, 4)
b)
(8, 15)
STEP 1: Draw in an angle in standard position, call the angle  , such that  has the smallest
possible positive measure and the given point is on the terminal side of  .
HINT: The angle must fit into a right triangle so it must be between 0 and 90 degrees.
Now using the same triangle that you have just created, make sure that you have all three sides to
identify the 6 trig functions – sine, cosine, tangent, secant, cosecant, and cotangent.
(-3, 4)
(8, 15)
Step 2: Use the Pythagorean Theorem to find the third side of the triangle.
Hypotenuse:
Hypotenuse:
Step 3: Now identify the values of the six trig functions for each angle in standard position having the
given point on the terminal side.
(-3, 4)
(8, 15)
sin  
csc 
sin  
csc 
cos  
sec  
cos  
sec  
tan  
cot  
tan  
cot  