SOLUTION: if sin of theta is equal to 2/3 and theta is in quadrant 1 what is the value of tan theta and cos theta ?

This approach might be more in line with what your teacher wants.

Draw angle theta in quadrant 1:



Draw a perpendiculat from the endpoint down to the x-axis:



Since the sine is the opposite over the hypotenuse, or y/r,
and the sine is given as 2/3, use the numerator 2 for y and the
denominator 3 for r

label the green line, opposite side y=2, and hypotenuse r=3



Now we use the Pythagorean theorem to find the adjacent side x,

r² = x² + y²

3² = x² + 2²
 
 9 = x² + 4

 5 = x²

√5 = x



tan(q) =  =  =  =  =   

cos(q) =  =  =  

Edwin