Question

If theta and phi are acute angles such that sin theta = 1/2 and cos theta is equal to 1/3 then Ï+phi lies in

Answer 1

Hi there,

I think there is some miss print in the question above. Hoping the correct question to be as follows:

If theta and phi are acute angles such that sin theta = 1/2 and cos phi is equal to 1/3 then theta+phi lies in?

Answer:

(θ+∅) lies in [π/2, 2π/3]

Step-by-step explanation:

We have  

sin θ = ½  

cos ∅ = 1/3  

Case 1 :

sin θ = ½  

sin θ will have its value as ½ in two quadrants I & II i.e., π/6 or 5π/6.

Since we are given that θ is an acute angle, therefore, here we get

θ = π/6 ….. (i)

Case 2:

cos ∅ = 1/3  

We know,  

0 < 1/3 < ½

∴ cos π/2 < cos ∅ < cos π/3

⇒ π/3 < ∅ < π/2 …… (ii)

Adding θ throughout (ii), we get

π/3+θ < ∅ + θ < π/2+θ

or, π/3+π/6 < ∅ + θ < π/2+π/6 ......... [from (i)]

or, π/2 < (∅ + θ) < 2π/3

Therefore, we can write

(∅ + θ) ∈ [π/2, 2π/3]

Hope this helps!!!!