Explanation:
11pi/6 in radians.
pi = 180°
so,
pi/6 = 180/6 = 30°.
11pi/6 = 11×pi/6 = 11×30 = 330° or -30°.
the reference angle is the smallest (measured in absolute values) angle to the horizontal (x) axis.
so, that is then 30°.
so, which statements are true, and which are false ?
1.
sin(330°) = -1/2, because the angle is in the 4th quadrant and therefore below the x-axis, which makes the sine values negative.
sin(reference angle = 30°) would be +1/2, but that was not the statement.
so, this statement is false.
2.
the reference angle is 60°.
since we can see that it is actually 30°, this statement is false.
3.
the reference angle is 30°.
yes, that is true.
4.
cos(330°) = sqrt(3)/2.
yes, that is true.
this cosine is on the right side of the y-axis and therefore positive.
5.
tan(330°) = 1.
as tangent = sine/cosine, to be equal to 1 means that sine = cosine. which is not the case here.
this statement is false.
6.
the reference angle is 45°.
no, as 3. had shown, it is 30°.
so, this statement is false.