Conversions and Rules

Question 1

Converting Degrees , Minutes, Seconds (DMS) to Degree Decimal Form

Answer 1

(1 degree / 60 min) , (1 degree / 36000 sec),

Question 2

Degree to Radians

Answer 2

(1 pi rad / 180 degrees)

*Whichever you are try to convert FROM (in this case Degrees) remember to put 180 degrees at bottom of ratio to cancel out the unity degrees.)

Question 3

Finding Coterminal angles

1. ) GIVEN : Angle in Degrees
2. ) GIVEN : Angle in Radians
   * remember to rationalize denominator if radical is present

Answer 3

If 750 degrees, the coterminal must be less or equal to 360. “ (360 x X ) “ must be near or less , but never greater than “given” angle.

IF: 750 - (360 x 1) = 390 (not < 360)
THEN: 750 - (360 x 2) = 30 (is < 360)

2.) IF: -5pi/6 + (2pi x 1 )=[12pi/6] = 7pi/6
THEN: Compare is 7pi/6 (is < 12pi/6 )

Question 4

Compute Arc Length

Given: Degrees and Radius

Answer 4

Arc Length = Angle (in Rad’s) * Radius

1.) Convert degrees given into Rad’s
105 degrees * (pi/ 180 degrees) = Angle in Rads
2.) Use found Rad’s * given Radius = arc length

Question 5

1. ) Angular Speed “W”

2. ) Linear Speed “V”

Answer 5

W= Angle (rad’s) / Time

V = Speed / Time 
AND 
V= Radius * Angle (rad's) / Time
or
V= W* Radius given 

**If Angle is given in degrees, convert to Rad’s
by dividing by 180 degrees

Question 6

Area of Part of a Circle “A”

Answer 6

A = .5 R^2 * Angle (rad’s)

**If Angle is given in degrees, convert to Rad’s
by dividing by 180 degrees

Question 7

Give: Known value of Trig function
Find: Other function values

Answer 7

Given : Cos = root5/3

This means the triangles lengths are =
Opp: ?
Adj: root5
Hyp: 3

To find Opp recall a^2 + b^2 = hyp^2
So: ?^2 + root5^2 = 3^2
cont: ?^2 = 9-5
?= 2

Question 8

Inverse SIN(root3/2)

Which Ø input results in output of Y=root3/2?

Answer 8

How to read this literally:
“What is inputØ brings an output of roo3/2. This given output MUST fall between the right side of the half moon for x value to be real”

I.E. it is the needing x value (not needed to give as answer to problem) that causes that domain restriction.