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Hi friends,

 

I hopefully have only 2 more questions for today. Both these questions come from the same problem. Please explain to me..please...

 

The 2nd step in the sum goes like this:

 

\({Sin135Cosx - Cos135Sinx} \over{Sinx}\)

 

becomes:

 

\({Sin45Cosx + Cos45Sinx \over Sinx}\)

 

How can this be?...sorry if I'm wasting someone's time with this one....sad..I tried to make the font a little bigger...unsuccessful.

 Mar 3, 2023
 #1
avatar+118617 
+1

Seems like you need to study up on the unit circle.

 

Here is a play page.

Its great if you already understand what you are looking at but maybe not so great if you don't.

 

https://www.mathsisfun.com/geometry/unit-circle.html

 

 

This video looks really good.   I have only watch about half but she sweemed to be explaining it really well.

 

https://online.clickview.com.au/exchange/channels/3010412/maths-with-heather-davis/playlists/3014610/trigonometry/videos/928592/lesson-12-angles-of-any-magnitude

 

 

summarizing.

If an angle is drawn on the unit circle as shown in the video, the hypotenuse of any triangle will be 1.

So 

cos of the angle is the x value on the circumference of the unit circle     So cos will be positive in the 1st and 4th quadrants

sin of the angle is the y value on the circumference of the unit circle      So sin will be positive in the  1st and 2nd quadrants

tan of the angle is the y value divided by the x value on the circumference of the unit circle      So tan will be positive in the  1st and 3rd quadrants

 

A sentance to help you with this is     ALL    Stations   To    Central

All trig values are positive for angles less than 90 degrees, that is angles in the 1st quadrant

Sin (but not cos or tan) will be positive for all angles in the 2nd quadrant,  that is angles between 90 and 180 degrees

Tan is positive in the 3rd quadrant

Cos is positive in the 4th quadrant.

 Mar 4, 2023
 #2
avatar+118617 
+1

so

 

sin135 = +sin (180-135)    Note:  it is in the secend quadrant fo it is positive

sin 135 = sin 45

 

Maybe you can try the rest yourself.

 Mar 4, 2023
 #3
avatar+1124 
0

my my my ...goodness!!!..off course!

 

gosh, you know what Melody...I have looked at for example Sin 140, as Sin 140 DEG, and therefore could not understand how on earth 135 DEGREES could be the same as 45 DEGREES

 

but yes, I see my error. Getting the actual values of the different Sin values, equate to the same answer....ALL RIGHTIE!!!...laugh 

 

Just a last thing...The different quads where the trig functions are either positive or negative, I fully understand, I use the phrase CAST, starting with quad 4...C=Cos, A=All, S=Sin and T=Tan...(obviously..laugh)

 

Thank you Melody for going through the trouble of finding those urls, I have not watched them, since I understand all of this, I just made a stupid error for mistaking the value for an angle...

 

I'm sending a BIG BUNCH of flowers!!

juriemagic  Mar 4, 2023
edited by juriemagic  Mar 4, 2023
 #4
avatar+118617 
0

I am glad I could help :)

Melody  Mar 4, 2023

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