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

option b

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)

Answer 2

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

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