The terminal side of #theta# lies on the line #4x+3y=0# in quadrant IV, how do you find the values of the six trigonometric functions by finding a point on the line?

1 Answer
Feb 3, 2017

Answer:

#sin theta= -4/5#; #cos theta= 3/5# ; #tan theta=-4/3# ; #sec theta =5/3#; #csc theta=-5/4# and #cot theta= -3/4#

Explanation:

The slope of the given line is #tan^ (-1) ( (-4)/3)# or #arc tan ((-4)/3)#. This means there is a point on this line with coordinates (3, -4). Its radial distance from the origin would be #sqrt(3^3 +4^2)# =5

The angle #theta# is, therefore, such that #tan theta= (-4)/3#.

As shown in the figure below, triangle OPM is a rt. triangle, its hypotenuse is 5 with base and altitude being 3 and -4 respectively. Accordingly,
#sin theta= -4/5#; #cos theta= 3/5# ; #tan theta=-4/3# ; #sec theta =5/3#; #csc theta=-5/4# and #cot theta= -3/4#

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