January 20 th BOOK 4.2 copyright2009merrydavidson.
-
Upload
claud-lane -
Category
Documents
-
view
213 -
download
0
Transcript of January 20 th BOOK 4.2 copyright2009merrydavidson.
January 20th BOOK 4.2 copyright2009merrydavidson
All Students Take Classes
Determine in which quadrant each trig function is positive.
QI: AllQII: sin/csc
QIII: tan/cot QIV: cos/sec
Trig Identities
f(x) = cos x f(x) = sin x
EVEN ODD
sin sinx x csc cscx x
cos cosx x sec secx x
Trig Identities
f(x) = tan x
ODD
tan tanx x
cot cotx x
Practice…
Follow the correct order of operations.
1. Find sin 180 (a quandrantal angle)
2. Find 3 cot 7/6
3. Find tan 120 + cot (-30)
4. csc /2 sin /2
3 3
0
3(cos/sin) =
3 3 2 3
1
Practice…
5) If cos (-t) = -1/5,
a) find cos (t) b) find sec (-t)
-1/5 -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.
14
Step 3: Use pythagorean Thm. To find the missing side.
15
Step 4: Use sohcahtoa to
find the missing trig values. Be sure to rationalize the denominator when necessary.
t
sin t = csc t =
cos t = sec t =
tan t = cot t = 15
154 15
15
41/ 4
15
4
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.
2
5
Step 3: Use pythagorean Thm. To find the missing side.
29Step 4: Use sohcahtoa to
find the missing trig values.t
sin t = csc t =
cos t = sec t =
tan t = cot t =
2 29
29
29
2
5 / 22 / 5
5 29
29
29
5
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 .
41(4,-5)
Step 1: draw what you know.
-5
4
Step 2: Find the hypotenuse.
Step 3: Use SOHCAHTOA to find what is asked.
sin = -5 / 41
cos = 4 /41 cot = -4/5
41
41
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