What is the csc, sec, and cot of point (3,4)?

1 Answer
Mar 22, 2018

Answer:

#"cosec " theta = h/o = 5/3#

#"sec " theta = h/a = 5/4#

#"tan " theta = a/o = 4/3#

Explanation:

If you have a point #P# at #(3,4)# you can draw a triangle from the origin.

A point cannot have a trig ratio, only an angle can. Assuming you mean the angle formed at #P#. Call it #theta#

The lengths of the sides will be as follows:

The horizontal line on the #x#-axis will be #3# units long.
This is the side opposite #theta#.

The vertical line along the line #x=3# will be #4# units long.
This is the side adjacent to #theta#

By Pythagoras, the hypotenuse from the origin to #P# will be #5# units.

NOw that we have the sides defined and we know their lengths we can determine the ratios.

#"cosec " theta = h/o = 5/3#

#"sec " theta = h/a = 5/4#

#"tan " theta = a/o = 4/3#