Homework Questions?
Jan 11­5:19 PM
Right Triangle Trigonometry ­­ almost the same as what we just did, but the sides are labeled differently. r = the hypotenuse = hyp
x and y are the opposite and adjacent sides, opp and adj, with order depending upon where you put the angle.
opp
sin θ =
hyp
hyp
csc θ = opp
cos θ =
adj
hyp
sec θ =
hyp
adj
tan θ =
opp
adj
cot θ =
adj
opp
where θ is either angle, α or β
β
hyp
hyp
opp
adj
α
adj
opp
Oct 5­5:09 PM
1
Let's find the exact values of the six trigonometric functions for 30
triangle with a base side of 1. sin 30
o
sec 30 o =
tan 30 o =
cot 30
o
and 60 o using our special
csc 30 o =
=
cos 30 o =
sin 60
o o
=
csc 60 o =
=
cos 60 o =
sec 60 o =
tan 60 o =
cot 60
o
=
Oct 5­5:57 PM
Now you find the exact values of the six trigonometric functions for 45
triangle with a base side of 1. sin 45
o
=
o using our special
csc 45 o =
cos 45 o =
sec 45 o =
tan 45 o =
cot 45
o
1
1
=
Jan 11­9:51 AM
2
You must memorize the exact values of sine, cosine, and tangent for 30 o, 45 o, and 60 o
There WILL be a quiz.
Jan 11­10:06 AM
β
α
Jan 11­9:54 AM
3
1. If α + β = 90 o, h ow do cos α and sin relate to each other?
2. How do cos β and sin Cofunctions:
β sin θ = cos (90
cos θ = sin (90
o
tan θ = cot (90
o
α relate to each other?
cot θ = (90
­ θ)
­ θ)
o
­ θ)
o
­ θ)
sec θ = csc (90
csc θ = sec (90
Why do you think this happened? Will it always happen?
o
­ θ)
o
­ θ)
Oct 5­5:40 PM
Jan 11­11:23 AM
4
Section 2.2
Angles can be divided into smaller pieces.
1 degree = 60 minutes and 1
o
1 minute = 60 seconds
= 60' 1' = 60"
Adding and subtracting in degrees, minutes, and seconds:
Add 42 o 12' 27" to 5
o
50' 3"
Subtract 18
o
43' from 25
o
5'
Jan 11­2:57 PM
Changing decimal degrees to degrees, minutes, seconds:
Example: change 25
Example: change 20.3
o
o
4' 15" to decimal degrees.
to degrees, minutes, seconds
Note: you may use your calculator to do these changes if you wish. From Decimal Degrees to Degrees, minutes, seconds is abbreviated DMS:
Try: 20.3 ­> DMS
From Degrees, minutes, seconds to Decimal Degrees is abbreviated Dec
Tru: 25
o
4' 15" ­> Dec
Jan 11­3:10 PM
5
Using your calculator to find trigonometric functions:
VIP: Make sure your mode is in degrees when the angle is in degrees.
If the angle is in decimal degrees, you can find sin, cos, or tan directly.
o
sin 55
=
cos 48.2
tan 78.72
o
=
o
=
To find csc, sec, or cot, use the reciprocal of sin, cos, and tan.
csc 48.1
o
sec 19.4
o
cot 8.75
o
= 1/sin 48.1
o
=
=
=
Jan 11­3:17 PM
If the angle is in degrees, minutes, seconds, you can use them directly, finding the appropriate symbols (often under math and angles or directly on the keyboard) on your calculator or you can convert them to decimal degrees first.
Find sin 32
o
10'48".
Jan 11­4:05 PM
6
Now for something more exciting! When an angle is between 0
what do you know about the signs of the trigonometric functions of that
angle?
o
and 90 o ,
If we have the value of a trigonometric function of an angle
between 0 o and 90 o we can use our calculators to find the
angle using the inverse trig functions:
sin -1 , cos -1 , and tan -1
sin A = 0.3971
A = sin
-1
0.3971
cos A = 0.5
tan A = 11.43
Jan 11­10:00 AM
If cot B = 0.4327, then we must find tan
B first.
tan B = 1/0.4327 and
B = tan -1 (1/0.4327) =
Jan 11­10:00 AM
7
Find the angle between 0
1. cos o
and 90
o
for each of the following.
C = 0.5490
2. tan A = 0.6273
3. csc B = 1.4293
4. sec D = 1.0801
Jan 11­4:23 PM
Now, look at problems 85­88 on p. 69. 85. What happens when you try to find calculator? Why does it happen?
A for sin A = 1.234 on your 86. What happens when you try to find Why does this happen?
B for sin B = 4.321 on your calculator? 87. What happens when you try to find tan 90
your calculator? Why does this happen?
o
88. What happens when you try to find cot 90
Why does this happen?
o
on on your calculator? Jan 11­10:04 AM
8
Jan 11­12:28 PM
9