Use identities to find the exact value of indicated trigonom

Use identities to find the exact value of indicated trigonometric function of the acute angle of theta. Sin theta = squareroot 3/3, cost theta = 2/3 Find Tan theta

Solution

Acute angle means the angle which is less than 90 degree

so that means theta is in first quadrant

so tan(theta) is positive

tan(theta) = sin(theta)/cos(theta)

= [ sqrt(5)/3 ] / [ 2/3 ]

= sqrt(5) / 2