Theory: Angles of magnitude (1 Viewer)

[MarsBarz]

I know angles of magnitude are a year 10 concept but after 2 years I have to admit that I am still having trouble understanding most of the theory behind them. I don't have any problems doing the angle of magnitude trig questions but it is the concept which I fail to fully comprehend. The proofs for angles of magnitude (ASTC) in the Maths in Focus book are absolutly incomprehensible.

I understand that angles are measured around a circle, starting from the positive direction of the x-axis. I also understand that all ratios are positive in the 1st quadrant because the y and x values are positive.

It's the other quadrants which confuse me. Can someone please explain the concept to me rationally and if possible using diagrams?

 

[Dumsum]

Easy way it was taught to us, remember that cos@ gives the x-value and sin@ gives the y-value.

1st quadrant: all positive as you said.

2nd quadrant: the x-value is negative, so cos(180-@) will be negative. y-value still positive, so sin(180-@) is positive. tan = sin / cos, +ve divided by -ve gives -ve, so tan(180-@) is negative.

3rd quadrant: both y- and x-values are negative. ie, cos(180+@) and sin(180+@) are both negative. tan = sin / cos, -ve divided by -ve gives +ve, so tan(180+@) is positive.

4th quadrant: y-value is negative, so sin(360-@) is negative, but x-value is positive, so cos(360-@) is positive. tan = sin / cos, -ve divided by +ve gives -ve, so tan(360-@) is negative.


If you want diagrams, just draw up a circle, and pick a point in each of the quadrants, you should be able to see.

 

[rama_v]

I know angles of magnitude are a year 10 concept but after 2 years I have to admit that I am still having trouble understanding most of the theory behind them. I don't have any problems doing the angle of magnitude trig questions but it is the concept which I fail to fully comprehend. The proofs for angles of magnitude (ASTC) in the Maths in Focus book are absolutly incomprehensible.

I understand that angles are measured around a circle, starting from the positive direction of the x-axis. I also understand that all ratios are positive in the 1st quadrant because the y and x values are positive.

It's the other quadrants which confuse me. Can someone please explain the concept to me rationally and if possible using diagrams?

You can also remember through drawing what the curves look like. E.g. for sin x you know that its positive (above y=0) between 0 and pi radians, you know that cos is positive from 0 to pi/2 and then from 3pi/2 to 2pi rad, and a similar situation can be applied to tan x as well.

 

[MarsBarz]

Thank you, it's a lot clearer now.

 

[munkaii]

Remember..all stations to cabramatta!

 

[insert-username]

Another way is to remember your number plane. I usually draw a little unit circle to help me visualise where my solutions will be - where X and Y are negative on the number plane, the corresponding ratios are also negative, etc.


I_F