Doubt in tutorial 8

[Meg]

Hello, I was confused as to which angles should be named theta and alpha as it was not given in the sum. Thank you! 

[Aisha Siddiqa]

I have the same question. How to know which angle is theta and which is alpha? 

If the angles were interchanged, would our answers change too? 

[Malabika Guha Mustafi]

Trying to give reply.

Theta is the angle of inclination ( angle between a line and x axis ) of a line. Theta is measured anticlockwise and right side of x axis. alpha is (180 degree- theta) , the adjacent angle of theta.  

tan alpha= - tan theta.

so, when a line makes an angle theta  with horizontal , for positive slope line , the slope is tan theta but for negative slope it is  tan alpha or  -tan theta .[Please draw two lines and corresponding theta , it will help you better to understand.)

[Meg]

Thank you for that but that was not the question. My question was which of the two angles should be names theta and alpha respectively as it is not mentioned in the question

[Malabika Guha Mustafi]

https://groups.google.com/a/nptel.iitm.ac.in/g/ma1001-discuss/c/FI63Kf3NiYM/m/BOzCxxFXAwAJ

[Malabika Guha Mustafi]

Team ,please response. 

[Malabika Guha Mustafi]

As per my understanding, 

Theta is  making acute angle (angle of inclination) when given  slope or m is positive.

so that alpha is obtuse angle and line is with a positive  slope.

Here, angle of inclination is acute.

 

but,  in negative slope the angle of inclination is obtuse, 

Here , m= tan (180 - theta)= -tan theta {angle of inclination is obtuse}.

It seems, in general theta is the interior angle of the triangle, opposite to the origin ( formed by angle of inclination and  two axis ).

Please,  wait for Team's response. 

 

[Mathematics 1 Support 2]

Dear learner,

Higher the value of tan value greater the proximity to the y-axis. Similarly higher the negative value of tan greater the proximity to the y-axis. Thus tan(theta)=-2 will be nearer to the building than tan(alpha)= -1.78. I hope this address your question. 

Malabika, those concept is right but for time being we don't have to get into deeper concept of trigonometry. Just simple realization of the nature of tan value will address the doubt asked. 

Thanks and regards 

Vicky Kumar Sharma 

Maths_1 instructor

IITM Online Degree 

[Malabika Guha Mustafi]

Exactly, higher slope value (Irrespective of sign ) means more steeper line (towards Y axix). Thank you  very much