A function value and a quadrant are given Find the other fiv

A function value and a quadrant are given. Find the other five function values. Give exact answers. sin theta = 1/7, Quadrant I cos theta = 4 Squareroot 3/7 tan theta = Squareroot 3/12 (Type an exact answer, using radicals as needed. Rationalize all denominators.) cos theta = 7 sec theta = 7 Squareroot 3 /12 cot theta = 4 Squareroot 3 (Type an exact answer, using radicals as needed. Rationalize all denominators.)

Solution

We have given sin(theta)=1/7,Quadrant I

cos(theta)=sqrt(1-sin²(theta))=sqrt(1-1/49)=sqrt(48/49)=(4*sqrt(3))/7

cos(theta)=(4*sqrt(3))/7

tan(theta)=sin(theta)/cos(theta)=(1/7)/((4*sqrt(3))/7) =1/(4*sqrt(3))

tan(theta)=1/(4*sqrt(3))

csc(theta)=1/sin(theta)=1/(1/7)=7

csc(theta)=7

sec(theta)=1/cos(theta) =1/((4*sqrt(3))/7)=7/(4*sqrt(3))

sec(theta)=7/(4*sqrt(3))

cot(theta)=1/tan(theta) =1/(1/(4*sqrt(3))) =4*sqrt(3)

cot(theta)=4*sqrt(3)