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

tan theta = - 3/4