If sin(theta)= -square root 2 /2 and tan(theta) = -1, (theta) measures, A) 45° B) 135° C) 225° D) 315°
I believe it is D. 315 degrees
Can you explain how you got the answer?
Sure! Well is the sin(x) = -sprt2/2 that means on the unit circle, that the y in the (x,y) is the whatever sin is. So we know that y=-sqrt2/2. And your tan(x)= -1 so that means that watever the x in the (x,y) is going to be positive because tan=sin/cos. And anything with a sqrt2/2 as the y is going to have the same as the x because the reference angle is 45.
With me so far?
So you look on the Unit Circle and find the angle with a reference angle of 45 and the coordinates of (sqrt2/2, -sqrt2/2) because the tan of those is -1. And you get the answer of 315 degrees.