Fill in the blank The smallest number c for which a function

Fill in the blank. The smallest number c for which a function f is periodic is called the of f. Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is In the correct mode.) tan 7 pi/9 Find the point (x, y) on the unit circle that corresponds to the real number t. t = pi/4 (x, y) = ()

Solution

The smallest number c for which function f is periodic is called period of f

Tan 7pi/9 = tan (pi-2pi/9)= -tan 2pi/9=-.8391

t=pi/4

X = r cos t

Since its a unit circle,therefore r=1

X= cos45 degree= sqrt2/2

Y=rsin t= sin45=sqrt2/2

Point is (sqrt2/2,sqrt2/2)