Precal for the Average Person

Table of Contents

1. Angles pg. 2 and 3

2. DMS and DD pg. 4

3. Reference Angles pg. 5

4. Sine, Cosine, Tangent pg. 6 and 7

5. Reciprocal Functions pg. 8

6. The Unit Circle and Quadrant Angles pg. 9

7. Unit Circle pg. 10

8. Using TI-82 and 83's to find Trig. Function Values pg. 11

9. Solving Right Triangle's pg. 12

10. Law of Sines and Law of Cosines and The Ambiguous Case

pg. 13

11. Trigonometric Ratios pg. 14 and 15

12. Area of Triangles pg. 16

13. Graphing Trig. Functions on the TI-83plus pg. 17

14. Phase Displacement pg. 18

15. Graphing Cosine and Sine trig. func. By hand pg. 19 and 20

16 Graphing Tangent and Cot trig. Func. By hand pg. 21 and 22

17. Self Evaluation pg. 23

Angles

Angles can be measured in three ways:

- Degrees

- Radians

- Revolutions (or rotations)

1 Revolution = 2π radians = 360 degrees

A positive angle rotates in a counter clockwise direction.

A negative angle rotates in a clockwise direction.

Revolutions:

Ð'ј CCW = __________________ 2 Ð'Ð... CW= _____________________

Ð'Ñ* rot CW= ___________________

1,3,4,7, and 9 are coterminal angles.

Circumference of a circle formula is C= 2 πR, therefore the central angle of 1 full revolution CCW corresponds to an arc length of S=2 πR.

Central angle Ө is measured in radians and has the formula Ө=S/R or S= R Ө

If 360 degrees = 2 π radians, then: 360/2π = 1 radian or 180/π.

To convert degrees to radians: multiply by π/180.

To change radians to degrees: multiply by 180/π.

Change 30 degrees to radians:

30/π * π/180 = π/6 radians.

Change 3/4π radians to degrees:

3/4π * 180/π = 135 degrees.

310 degrees = 31/18π

3/2π = 270 degrees.

DMS and DD

1 degree contains 60 minutes. 1 minute contains 60 seconds.

- DMS means degrees, minutes, seconds

- DD means decimal degrees.

- To convert DD to DMS just enter the DD value, hit 2nd angle, choice 4 (DMS), enter, and you'll get DMS.

- To convert DMS back to DD on a TI-82, enter as follows:

10 degrees 15'30" will be entered as:

10 + 15/60 + 30/3600=

and you'll get the DD result.

- To convert radians to degrees you first convert the radians, then you have DD. If you need DMS you can use your calculator, as stated above.

DD ex = 25.62 degrees

DMS ex = 5 degrees 30'30"

DMS to DD = 5 + 30/60 + 30/3600 = 5.5083 degrees

The complement of 35 degrees 45'10"

90 degrees 60'60"

- 35 degrees 45'10"

= 54 degrees 14'50"

The Supplement of 60 degrees 29' 35"

180 degrees 60'60"

- 60 degrees 29'35"

= 119 degrees 30'25"

The complement of π/4 rad.

π/2 Ð'- π/4 = 2/4π Ð'- π/4 = π/4

The supplement of π/4 = 3/4π

Reference Angles

If Ө is in Q1, then Ө is its own ref. angle.

If is in Q1, then is its own ref. angle.

If Ө is in Q2, then 180 degrees - Ө is the ref. angle.

If is in Q2, then π- is the ref. angle.

If