In ∆PQR, ∠Q is a right angle PQ = 3, QR = 4. If ∠P=α and ∠R=β, then find the values of

(i) sin α (ii) cos α

(iii) tan α (iv) sin β

(v) cos β (vi) tan β

Given : PQ = 3, QR = 4

⇒ (PQ)² + (QR)² = (PR)²

⇒ (3)² + (4)² = (PR)²

⇒ 9 + 16 = (PR)²

⇒ (PR)² = 25

⇒ PR =√25

⇒ PR =±5

But side PR can’t be negative. So, PR = 5

(i) sin α

We know that,

Here, θ = α

The side opposite to angle α = QR =4

Hypotenuse = PR =5

So,

(ii) cos α

We know that,

Here, θ = α

The side adjacent to angle α = PQ =3

Hypotenuse = PR =5

So,

(iii) tan α

We know that,

Here, θ = α

Side opposite to angle α = QR =4

Side adjacent to angle α = PQ =3

So,

(iv) sin β

We know that,

Here, θ = β

The side opposite to angle β = PQ =3

Hypotenuse = PR =5

So,

(v) cos β

We know that,

Here, θ = β

Side adjacent to angle β = QR =4

Hypotenuse = PR =5

So,

(vi) tan β

We know that,

Here, θ = β

Side opposite to angle β = PQ =3

Side adjacent to angle β = QR =4

So,