Download Unit 6.0

MA42: TRIGONOMETRY & COLLEGE MATH
CALCULATOR: ANGLES & THEIR MEASURES
I.
Degree / Radian Measure
When working with angle measures, it is important that your calculator is using the appropriate
measure (Degree or Radian).
B.
To set the calculator to the appropriate measure:
1.
2.
3.
4.
C.
II.
LESSON NOTES
Press [mode]
Move cursor to the third row.
Place cursor on the desired measure
Press [enter]
Exercises:
1.
What angle measure (Degree or Radian) is your calculator currently using?
2.
If in Degree mode, change to Radian.
If in Radian mode, change to Degree.
Change Decimal Degree Form  Degreeº Minute’ Second” Form
At times, you may want to rewrite an angle measure expressed in decimal degree form (i.e.
125.34º) into Degreeº Minute’ Second’’ form (DMS) (125º 20’ 24”) or from DMS form to decimal
degree form.
A.
To change  from decimal degree form to DMS form:
1.
2.
3.
4.
5.
B.
Type angle.
Press [2nd] [angle].
Move cursor to 4:›DMS & press [enter].
The angle you typed will appear with ›DMS next to it.
Press [enter] again.
To change  from Degreeº Minute′ form to Decimal Degree Form.
1. Type the Degree part
2. Press [2nd] [angle].
3. Move cursor to 1:º & press [enter]
4. The angle appears with a degree symbol
5. Type the Minute part
6. Press [2nd] [angle]
7. Move cursor to 2:′ & press [enter]
8. The angle appears with a degree symbol and minute symbol
9. Press [2nd] [angle]
10. Move cursor to 1:º & press [enter]
11. The decimal degree form is listed
C.
Exercise:
1. Change the following angles from decimal degree form to Degreeº Minute’ Second’’
form (DMS).
a. 35.27
b.  147.35
c. 278.81
2. Change the following angles from DMS form to decimal degree form.
a. 23417'
b.  1856'
c. 9130'
III.
Approximate the Six Trigonometric Functions using Calculators
The calculator can be used to find the approximate value of the Six Trigonometric Functions.
The approximations are written in decimal form and in most cases are approximations because
they are rounded.
A.
Approximate the sin  , cos  , and tan  .
The calculator has buttons that correspond to the sine, cosine, and tangent functions.
Values of these functions can be calculated directly using these buttons.
1.
To calculate the sine, cosine, and tangent of  .
1.
2.
3.
4.
Be sure the calculator is set at the desired mode (degree or radian).
Press [sin] for sine, [cos] for cosine, [tan] for tangent.
Type the angle measure.
Press [enter]
2. Exercise: Approximate the sin  , cos  , and tan  for each value of  .
2

a. 37
b.
c. 149.32
d. 
7
3
B.
Approximate the csc  , sec  , and cot  .
The calculator does NOT have buttons for cosecant, secant, and cotangent functions.
Value of these functions must be calculated indirectly using the Reciprocal Identities.
1.
The Reciprocal Identities we will use are:
csc 
2.
sec 
cot  
To calculate the cosecant, secant, and cotangent of  .
To Find Cosecant
Type [1] [÷] [sin]
Type the angle measure
Press [enter]
To Find Secant
Type [1] [÷] [cos]
Type the angle measure
Press [enter]
To Find Cotangent
Type [1] [÷] [tan]
Type the angle measure
Press [enter]
OR
To Find Cosecant
Type:
[ ( ] [sin] [angle] [ ) ] [ ) ] [ x
Press [enter]
To Find Secant
Type:
1
]
[ ( ] [cos] [angle] [ ) ] [ ) ] [ x
Press [enter]
To Find Cotangent
Type:
1
]
[ ( ] [tan] [angle] [ ) ] [ ) ] [ x
Press [enter]
3. Exercise: Approximate the csc  , sec  , and cot  for each value of  .
2

a. 37
b.
c. 149.32
d. 
7
3
1
]
IV.
Find the Angle  Given the Value of a Trig Function using Calculators
The calculator can be used to find the value of an angle given the value of one of it’s Six
Trigonometric Functions.
A.
Find the angle  given the value of sin  , cos  , or tan 
The calculator has buttons that correspond to the sine, cosine, and tangent functions.
Above these keys (2nd function button) are symbols for [ sin 1  ], [ cos 1  ], and [ tan 1  ]
respectively. These 2nd function buttons are used to calculate  .
1.
To calculate the angle  given the value of sin  , cos  , or tan  .
If sin  is known
If cos  is known
If tan  is known
Press [2nd] [sin]
Type the value of sin 
Close parenthesis [ ) ]
Press [enter]
Press [2nd] [cos]
Type the value of cos 
Close parenthesis [ ) ]
Press [enter]
Press [2nd] [tan]
Type the value of tan 
Close parenthesis [ ) ]
Press [enter]
2. Exercise: Find the angle  given the value of sin  , cos  , or tan  .
a. sin   0.6018
b. cos   .6235
c. tan   0.5933
d. sin   .8660
B.
Find the angle  given the value of csc  , sec  , and cot  .
The calculator does NOT have buttons for cosecant, secant, and cotangent functions.
The angle  must be calculated indirectly using the Reciprocal Identities.
1.
The Reciprocal Identities we will use are:
csc  
2.
sec 
cot  
To calculate the cosecant, secant, and cotangent of  .
If csc  is known
If sec  is known
Press [2nd] [sin] [ ( ] [1 / ]
Type the value of csc 
Press [ ) ] [ ) ]
Press [enter]
Press [2nd] [cos] [ ( ] [1 / ]
Type the value of cos 
Press [ ) ] [ ) ]
Press [enter]
If cot  is known
Press [2nd] [tan] [ ( ] [1 / ]
Type the value of tan 
Press [ ) ] [ ) ]
Press [enter]
OR
If csc  is known
Press [2nd] [sin] [ ( ]
Type the value of csc 
Press [ ) ] [ x 1 ] [ ) ]
Press [enter]
If sec  is known
Press [2nd] [cos] [ ( ]
Type the value of cos 
Press [ ) ] [ x 1 ] [ ) ]
Press [enter]
If cot  is known
Press [2nd] [tan] [ ( ]
Type the value of tan 
Press [ ) ] [ x 1 ] [ ) ]
Press [enter]
3. Exercise: Find the angle  given the value of csc  , sec  , or cot  .
a. csc   1.662
b. sec   1.604
c. cot   1.685
d. csc   1.154