Question

If tan theta is equal to minus 4 by 3 then sin theta is

Answer 1

Answer: sinθ= ±4/5

Step by step explanation:

tanθ = -4/3 = height/base

By pythagoras theorem,

(Hyp.)² = (-4)² + (3)²

(Hyp.)² = 16+ 9 = 25

(Hyp.) = √25 = ±5

Then,

Hypotenuse = ±5

Height = -4

Base = 3

sin θ = height/hypotenuse 

sin θ = ±4/5

Answer 2

Answer :-

sin θ = ± 4/5

Explanation :-

Given

tan θ = - 4/3

We know that

sec² θ = 1 + tan² θ

sec² θ = 1 + (-4/3)²

sec² θ = 1 + (-4)²/(3)²

sec² θ = 1 + (16/9)

sec² θ = (9 + 16)/9

sec² θ = 25/9

1/cos² θ = 25/9 [ ∵ sec² θ = 1/cos² θ]

cos² θ = 9/25

We know that

sin² θ = 1 - cos² θ

sin² θ = 1 - (9/25)

sin² θ = (25 - 9)/25

sin² θ = 16/25

sin θ = ± √(16/25)

sin θ = ± √(4/5)²

sin θ = ± 4/5