January 20th
BOOK 4.2
copyright2009merrydavidson
All Students Take Classes
QII: sin/csc
QI: All
Determine in
which quadrant
each trig
function is
positive.
QIII: tan/cot
QIV: cos/sec
Trig Identities
f(x) = cos x
EVEN
cos   x   cos x
sec   x   sec x
f(x) = sin x
ODD
sin   x    sin x
csc   x    csc x
Trig Identities
f(x) = tan x
ODD
tan   x    tan x
cot   x    cot x
Practice…
Follow the correct order of operations.
1.
Find sin 180 (a quandrantal angle)
0
2.
3.
4.
Find 3 cot 7/6
3(cos/sin) =
3 3
Find tan 120 + cot (-30)
csc /2 sin /2
  3  3  2 3
1
Practice…
5) If cos (-t) = -1/5,
a) find cos (t)
-1/5
b) find sec (-t)
-5
Given 1 trig function, find the value
of the remaining 5.
6) sin (t) = ¼, find the remaining values.
Step 1: ¼ is positive so draw a right triangle in
quadrant I because sine is positive in quadrant 1.
Step 2: Label opposite and hypotenuse.
Step 3: Use pythagorean Thm. To find the missing side.
4
Step 4: Use sohcahtoa to
find the missing trig values.
Be sure to rationalize the
denominator when
necessary.
1
t
15
sin t =
1/ 4
csc t =
4
cos t =
15
4
sec t =
4 15
15
tan t =
15
15
cot t =
4 15
15
Given 1 trig function, find the value
of the remaining 5.
7) tan (t) = 2/5; find the remaining values.
Step 1: 2/5 is positive so draw a right triangle in
quadrant I because tangent in positive in QI.
Step 2: Label opposite and adjacent.
Step 3: Use pythagorean Thm. To find the missing side.
Step 4: Use sohcahtoa to
find the missing trig values.
29
t
5
2
sin t =
2 29
29
csc t =
29
2
cos t =
5 29
29
sec t =
29
5
tan t =
2/ 5
cot t =
5/ 2
EX 8: The terminal side of an angle with measure 
in standard position passes through (4,-5). Sketch
the reference angle. Evaluate sin , cos , and cot .
Step 1: draw what you know.
Step 2: Find the hypotenuse.
Step 3: Use SOHCAHTOA to
find what is asked.
4

41
-5
(4,-5)
sin  = -5 41/ 41
cos  = 4 41/41
cot  = -4/5
EX 9: Terminal side of an angle with measure ,
in standard position, ending at (-4,7).
Evaluate all six trig functions.
EX 10:  is given in standard position in QII and
sin  = 2/7, find cos , tan , and sec .
In QII the x value is NEGATIVE
EX 11:  is in standard position in quadrant III,
and tan  = 2/5. Find sin , csc  and cot .
In QIII the x value and
y value’s are NEGATIVE!
The radius is ALWAYS positive.
Quiz Monday over:
•
•
•
•
•
•
•
•
•
Fill in a blank unit circle with everything.
Give the (x,y) ordered pairs for specific radian values.
Give the sine/cosine at certain radian values.
Given a specific trig value, find the other 5 trig values.
Given a point on the terminal side of an angle, find the 6
trig functions.
Know which trig functions are even and odd.
Know the period for all 6 trig functions.
Given a right triangle, find 2 of the sides and/or 2 of the
angles using SOHCAHTOA.
Answer 2 application problems using SOHCAHTOA.
HW: WS 6-6
study for quiz