Trigonometric Angles

[Khoxy]

Convert the following anles to radians as multiples of π.

(a) 540° (b)-111°

Solution.

540° × π/180° = 3π

 

-111 × 1/180° = -37π/6

 

One thing I don't understand is presenting the answer as the multiples of π. May someone help please!

Edited May 10, 2019 by Khoxy

[GAHD]

1st: you might understand the number play you're doing with degrees and Pi better if you understand differentials a bit better, you're not arranging the variable right...

radian = taking the radius of the circle(center to edge distance) and wrapping it around the outside. Wrapping that radian around the circle 3.14159(etc) times gets you halfway around the circle. if you wanted to get all the way around the circle, you'd repeat  6.28318(etc) times. So half a circle (180 degrees) is the same as 1Pi measuring along the outside, and a full circle is 2Pi(or one Tau). Everything in between can be chopped up into fractions, 1/4 circle is 1/4 of 2Pi so 2Pi/4 or Pi/2.

It might be easier to understand in terms of Tau, since that's less messy. But that'll probably make your teacher go nuts.

[OceanBreeze]

 

The angry old man is just the way I feel about those two youtube videos. I only lasted about 1 minute on each. The woman narrator of the first sounded like she was on speed and the man in the second was on acid.

Edited May 11, 2019 by OceanBreeze

[exchemist]

Convert the following anles to radians as multiples of π.

(a) 540° ( :cool:-111°

Solution.

540° × π/180° = 3π

 

-111 × 1/180° = -37π/6

 

One thing I don't understand is presenting the answer as the multiples of π. May someone help please!

Yes it's to get you think in radians, which is what you need for more advanced mathematics.

 

When you start manipulating functions such as Sin x, it makes little sense to think of x in terms of degrees. You need to think of 90 deg as π/2, 180deg as π and 270deg as 3π/2, etc, because those are the values of x as a number that correspond to the function Sin x taking the value 1, 0 and -1 etc.

 

You need this sort of thing to represent waves, for instance. x can take any value you like and the Sin x function oscillates repeatedly between 1 and -1 with a wavelength of 2π.    

[Khoxy]

So you mean I have not really worked out for the solutions?

[OceanBreeze]

You will appreciate this sort of problem more when you learn that understanding why things are done a certain way is far more important than just getting a correct answer to the question.

 

I thought exchemist's explanation was right on point. You may want to read it again and really try for understanding.

 

Incidentally, take another look at your second example. Do you see a π in your conversion factor?

 

[GAHD]

So you mean I have not really worked out for the solutions?

yeah, cause -111 (just over 1/4 turn clockwise) is NOT anywhere near -37Pi/6 (little over 3 turns clockwise) You did that math WAY wrong. Watch the tau vids I linked, second one especially around 5 mins in.

 

It helps when you can picture a circle in your mind with a few marks on it and learn to rotate it around the way the math describes.

 

It also helps when you understand what Pi and Tau ARE: ratios

 

 

The angry old man is just the way I feel about those two youtube videos. I only lasted about 1 minute on each. The woman narrator of the first sounded like she was on speed and the man in the second was on acid.

That's sad. The second one gets into nitty gritty just past 5 mins. You can get the paper version easily enough by looking up the Tau Manifesto

 

The first one is totally ramble-tastic drawing many disparate threads of thought into the narrative, but that's half the joy of it to me. Probably the late 20's early 30's angsty nerd rants that make me smile with nostalgia.

Edited May 12, 2019 by GAHD
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