MAT & Trig
Opener
Mathematician:
Use the reciprocal identities to find each function value.
1) If sec  
3
, find cos  .
4
Identify the quadrant or quadrants for the angle satisfying the given conditions.
2)
sin   0
tan   0
3)
csc   0
cos   0
Give the signs (positive or negative) of the sine, cosine, and tangent functions for each angle.
4)
298o
5)
195o
Sine:
Sine:
Cosine:
Cosine:
Tangent:
Tangent:
Find the indicated function value using the given value.
6)
Find the value of cos  in Quadrant II if tan   
12
.
5
MAT & Trig
Notes 1.4 Part 2
Mathematician:
PART I – Expanding our understanding of the Signs Associated with the Six Trig Functions
During our discussion yesterday, we discussed how each of the trig functions can change from
positive to negative depending on what quadrant you are looking at. The shortcut to remembering
the pattern was: _______________________________________________
EX: Give the signs (positive or negative) of the sine, cosine, and tangent functions for each angle.
Sine: 39° Sine: Cosine: Tangent: ‐ 75° Sine: 207° Cosine: Cosine: Tangent: Tangent: Rather than ask about all six trig functions, we might ask you to find one specific ratio at a time.
EX:
Find the indicated function value using the given value.
3
4
Find cos  , if tan    , with  in QII
Find csc  , if cos  
1
, with  in QIV
2
PART II – Identifying RECIPROCAL Trig Functions
Before we begin our discussion, what does the math term reciprocal actually mean?
We know that sin  
opposite
hypotenuse
, and we also learned during this unit that csc  
.
hypotenuse
opposite
Therefore, it follows that sin  
1
. We call this a reciprocal identity.
csc 
Reciprocal Identities
sin  
cos  
tan  
csc  
sec  
cot  
Find each function value using the appropriate reciprocal identity.
a) Find cos  , if sec  
5
3
b) Find sin  , if csc   
c) Find cot  , if tan   5
12
2