Math - Radians and Degrees - Challenge

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#21

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#22
  1. 120° into Rad.

120° x τ/360 = Θ
Θ = τ/3

120° x π/180 = Θ
Θ = 2/3π

  1. Convert to degrees.

τ/8 x 360/τ = Θ
Θ = 45°

π/4 x 180/π = Θ
Θ = 45°

#23

Ok! Here we go:

  1. Convert 120 deg to rad:

Pi/180 x a = Theta
Theta = Pi/180 x 120
Theta = 2Pi/3

  1. Convert Pi/4 to degrees

Theta = 180/Pi x a
Theta = 180/Pi x Pi/4 = 45 degrees

#24

120 deg → t/3 or Pi/1.5 = 2.09…
deg * t / 360 = rad
120 * ((2*Pi) / 360) = 2.0943

t/8 → 45 deg
t/8 = 0.7854
t/8 * (360 / t) = deg
(0.7854) (57.2958) = 45 deg

You have no idea how hard it has been for me to work between degrees and radians, and now I can do the math in my head… I got my money’s worth already. :sob:

#25

1)120degrees=tau/3=2pi/3
2)tau/8=pi/4=45degrees

Theta had me a bit confused there. Hopefully I ahve the understanding right in that a full circle is: Theta=360degrees=tauRads=2piRads. I’d almost prefer to ignore the Theta part of it completely.

#26

guess is 2 radians
guess for 2 is 45 degrees

120 degrees to radians = 120/pi x pi/180 = 1.5
pi/4x180/pi =45 degrees

#27

Guesses:
1.) 2π/3
2.) 40°

Calculations:
1.) θ * π/180 = 120π/180 = 2π/3
2.) θ * 180/π = π/4 * 180/π = 45°

#28
  1. 120 * π / 180 = 2/3 π Rad
  2. π * 180 / 4 * π = 45 Deg
#29

Challenge

Convert 120deg to rad, then convert τ/8 to degrees

(120) * ( τ/360) = θ

τ/3 = θ

(τ/8) * (360/τ) = θ

45 = θ

#31

The radians are τ/3 because 120 is third of a circle

  1. 120 * τ/360 = θ
    θ = τ/3

  2. τ/8 * 360/τ = θ
    θ = 45

#32

I have never even heard of radians before this lecture, so conceptually I am sure I got this very wrong. Here we go:

NOTE: I use 3.14 as the value for Pi.

1.) Guess for 120° to Radians: 1/3

	120 * (π / 180) = Θ
	120 * (0.01744) = Θ
			 2.0928 = Θ || 2.0944rad
	


2.) Guess for (τ / 8) or (π / 4) to Degrees: 90°

	(π / 4) * (180 / π) = Θ
	0.785   * 57.32     = Θ
					45  = Θ || 45°
#33

This seems more complicated in the video
1 Tau = Circumference = 360 degrees = 6.28 Radians
1 Rad is 57.295 in degrees

  1. 120*d / 57.295 = X(Radians)
    A / Rad = X (where A is the Variable to convert, Rad is a constant)

  2. (6.28(T) / 8) * Rad = X(Degrees)
    T (constant) / A-Variable * Rad (constant)
    There is a Simpler Way:
    1 Tau = 360 therefore: 360/8 = Answer in degrees

There is probably a direct relationship / pattern between the two but my brain is melting :smiley:
6.28/360 = 0.0174 * (Degrees) = Radians
360/6.28 = Rad (in degrees 57.32) Radians: Rad * (Radians to convert) = Degrees

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#34

Here’s my answers for the Radians and Degrees challenge:
Q1. Given an angle of 120 degrees, convert to radians

A1. (1/3)τ

Q2. Given (τ/8), convert to degrees

A2. 45 degrees

A1a. (τ/360) * 120
A1b. (120τ/360)
A1c. (1/3)τ

A2a. (360/τ) * (τ/8)
A2b. (360τ/8τ)
A2c. 360/8
A2d. 45

I am thoroughly enjoying using tau (τ). I’m almost flabbergasted that at any point in my educational career I was taught pi - I’m having revelations of understanding that I’ve been struggling with for 15 years now. This might be the most helpful, enlightening, and interesting lecture so far! I am now a huge proponent of tau and will be singing its praises every chance I get.

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#35

i did not understand the guessing part like you means calculate in your head or something. Oh now I understand. like 120 is 1/3 of 360 and Tau = 360 then 120 is = 1/3 of tau and it is tau/3

#36

1. convert 120 deg to radians

120 * tau/360 = tau/3 or 2.09

2. convert tau/8 to degrees

tau/8 * 360/tau = 360/8 = 45

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#37

Convert 120 degree to Rad

For Tao:

  Tao/360 * 120 = Tao/3 
  
  Tao = 2 * Radius(3.14)
   
   2 * 3.14 / 3 = 2.0933

For Radius:
 
  Radius/180 * 120 = Radius/1.5
 
  Radius = 3.14

   3.14/ 1.5 = 2.0933

  1. Tao/8

    Tao/8 * 360/Tao = 45

    Pi/4 * 180/Pi = 45

#38

For section 2, 180/PI is 57.3, not 45 and PI/4 is 0.707 which the sin-1 will give you 45. Might I recommend you review this video again.

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