Question

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

Answer 1

Answer:

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

Answer 2

Answer:

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)