Question

there is a point which lies in quadrant 1 and is on the unit circle. the x-coordinate for this point is 1/4 determine the y-coordinate and then determine the value of tan theta

Answer 1

There is a point which lies in quadrant 1, then:
x>0 (positive) and y>0 (positive)

and is on the unit circle, then:
Radius: r=1

the x-coordinate for this point is 1/4:
x=1/4

determine the y-coordinate:
y=?
y=sqrt(r^2-x^2)
y=sqrt[(1)^2-(1/4)^2]
y=sqrt(1-(1)^2/(4^2)]
y=sqrt(1-1/16)
y=sqrt[16-1)/16]
y=sqrt(15/16)
y=sqrt(15)/sqrt(16)
y=sqrt(15)/4

determine the value of tan theta
tan theta=y/x
tan theta=[sqrt(15)/4]/(1/4)
tan theta=sqrt(15/4)*(4/1)
tan theta=sqrt(15)

Answers:
y=sqrt(15)/4
tan theta=sqrt(15)