If cos theta 4/5 and theta lies in quadrant 2, what is the value of tan theta?
1)3/4 2)4/3 3)-3/4 4)-4/3

The answer to your question is the third choice -3/4

Step-by-step explanation:

Data

cos Ф = 4/5

second quadrant

Process

1.- In the second quadrant cosФ is negative.

2.- cosФ relates the adjacent side and the hypotenuse

               cos Ф = adjacent side / hypotenuse

Then,         Adjacent side = 4      hypotenuse = 5

3.- Calculate the Opposite side using the Pythagorean theorem

                c² = a² + b²

                5² = 4² + b²                    

               25 = 16 + b²

                b² = 25 - 16

                b² = 9

                b = 3

Opposite side = 9

4.- The tangent relates the Opposite side and the Adjacent side

              tan Ф = Opposite side/Adjacent side

              tan Ф = 3/4

but it is negative in the second quadrant

              tan Ф = -3/4

Step-by-step explanation:

since theta is in second quadrant tan value is negative

COS is 4/5 (adjacent/hypotenuese)

(adj)²+(opposite)²=(hypo)²

4²+(opposite)²=5²

opposite side=√9=3

tan thet=3/4

but theta is in second quadrant

hence

the answer to the expression is 83