SOLUTION: Find the value of the five other trig functions, given sinx=square root -2/2 and cosx<0 also give degree and radian measure of x

I will use a capital X to represent the angle, and a 
small x to represent the x-coordinate in the graph.
Don't get them confused!

Since


and that is a negative number, this tells us that 
the angle X is in either QIII of QIV.

Since


that tells us that the cosine is a negative number,
and we know that the cosine is negative in QII and QIII,

so therefore we know that angle X is in QIII, so we
draw it:



Since the sine is , we take the
numerator of the given sine, which is  to be the 
value of y, and the denominator 2 to be the value of r.



Next we calculate the value of x (small x) using the Pythagorean
theorem:







We know to take the velue of x as negative, because
x goes left from the origin, so


and we label it thusly:



Now we get the other 5 trigonometric functions by using
the definitions:











Since the right triangle has two legs equal it is isosceles
are the reference angle is therefore 45°.

Since the angle is in QIII, we must add 180° to its
reference angle, so

the angle X in degree measure is 45°+180° or 225°

In radian measure, we multiply by 




Edwin