If sin theta=-3/5 and cos theta>0, what is the value of tan theta?

1) 3/4 2) - 3/4 3) 4/3 4) - 4/3

option b

Step-by-step explanation:

Consider a right angled triangle ABC

BI/

I /

I /

AI__/C

let theta be at angle C

sin theta=-3/5 (opposite/hypotenuese)

AB²+AC²=BC#

9+AC²=25

AC=√16=4

hence

tan theta = - 3/4 (opposite/adjacent)

The answer to your question is the second choice tan Ф = - 3/4

Step-by-step explanation:

Data

sin Ф = - 3/5

cos Ф > 0

Process

1. - The sin Ф is negative, which means that is in the third or fourth quadrant.

2. - sin Ф = - 3/5 and sin Ф = Opposite side/hypotenuse

then, Opposite side = 3 hypotenuse = 5

3. - Calculate the adjacent side using the Pythagorean theorem

c² = a² + b²

b² = c² - a²

b² = 25 - 9

b² = 16

b = 4

4. - If cos Ф is in the third quadrant

cos Ф = - 4/5 and cos Ф < 0 This is incorrect

5. - If cos Ф is in the fourth quadrant

cos Ф = 4/5 and cos Ф > 0 This is correct

Then, this angle is in the fourth quadrant

6. - Calculate tan Ф

tan Ф = - 3/4