Isaiah L.

asked • 04/19/16

Does -79 degrees equal 101 degrees when using tan^-1 to find the angle in a linear graph?

I need to find the acute angle of the equations y= 4x+4 and y=-5x+19. I do this drawing a horizontal line at the intersection point and finding the angles of both the lines (from the line to the line at the intersection point) then subtracting them. The problem is that I used tan-1-5 to find the angle of the second line but it gave me ≈-79o. The CAS Program I used to plot the graph said that the angle is 101o. Does this mean if I use a negative gradient with tan-1, I just subtract the angle by 180o  and that is the angle?
 
 

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Richard B. answered • 04/19/16

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Yes. They have the same reference angle (79 degrees) and the same sign. (the angles are in the 2nd and 4th quadrants respectively and in both of these tangent is negative.)
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Kenneth S.

1.  Remember than, for the tangent function to have an inverse, there must be a restriction on which angles are used; the interval chosen is (-pi/2,pi/2) so that the function is strictly increasing and thus 1 to 1 and therefore has an inverse. This means that, for any tan-1operation, the output can only be in 4th or first quadrants. 
2. The human adjustment after the above operation is to ADD 180o to the answer (in degrees) obtained from using the inverse tangent function, where necessary.  From an English usage standpoint, you don't SUBTRACT BY 180; you subtract a number FROM another.  BUT THE RIGHT WAY TO 'CORRECT' A NEGATIVE, 4TH QUADRANT RESULT IS TO ADD 180.
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04/19/16

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