How do you find x if the point (x,-3) is on the terminal side of theta and #sintheta=-3/5#?

1 Answer
Mar 4, 2017

Answer:

#x = +- 4#

Explanation:

By the definition of sine, we have

#sintheta = "opposite"/"hypotenuse" = -3/5#

Therefore, the side opposite #theta# measures #-3# units and the hypotenuse measures #5# units. These can be seen as dimensions on a right angled triangle, so we have, by pythagoras:

#5^2 - (-3)^2 = a^2# where #a# is the side adjacent #theta#

#25 - 9 = a^2#

#a = sqrt(16)#

#a = +- 4#

The side opposite #theta# is always the #y#-value, while the side adjacent #theta# is always the #x#-value. Therefore, #x = +- 4#.

We can't specify whether it is #x = +4# or #x= -4# unless you give us the quadrant (e.g. Quadrant III, or Quadrant IV).

Hopefully this helps!