Given sin theta = 1/3 and 0 theta pi/2 find tan 2 theta

Step-by-step explanation:

Given:

Theta lie in first quadrant.

Multiply both sides by 2

2theta lie in I and II quadrant.

is positive in I and negative in II quadrant.

Hence, The value of

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: