Download Notes 1.4 Day 1.jnt

College Math Survey
Notes 1.4 Part 1
Mathematician:
09.01.15
Part I – Revisiting the Six Trig Functions
BEFORE
NOW
PROBLEM: Given (-3,4) find all six trig
functions.
4
in quadrant II,
5
find all six trig functions.
Draw the Shape
Draw the Shape
Find the remaining side:
a 2  b2  c2
PROBLEM: Given sin  
Find the remaining side:
a 2  b2  c2
Label the hypotenuse, opposite & adjacent!
Label the hypotenuse, opposite & adjacent!
Write all six trig ratios.
Write all six trig ratios.
sin   ___
csc   ___
cos   ___
sec   ___
tan   ___
cot   ___
sin  
4
5
csc   ___
cos   ___
sec   ___
tan   ___
cot   ___
EX1: Find the values of all six trig functions for each angle in the given quadrant.
cot  
5
,
12
lies in QIII.
EX2: Find the values of all six trig functions for each angle in the given quadrant.
cos   
3
,
4
lies in QII.
Part II – Revisiting the Signs (positive or negative) for each of the Six Trig Functions
You may have noticed that the signs associated with these values are pretty important. In order
to keep better track of signs, many trigonometry students use the acronym ALL STUDENTS TAKE
CALCULUS.
In practice, the acronym follows the four quadrants like so:
S
A
T
C
A: All trig functions are positive (sin, cos, tan)
S: sine is positive
T: tangent is positive
C: cosine is positive
EX3: Identify the quadrant or quadrants for the angle satisfying the given conditions.
sin   0
sec   0
Ex 4: Identify the quadrant or quadrants for the angle satisfying the given conditions.
sin   0, cos   0
tan   0, sec   0