Question

If sin θ = 3/5 , find the values of other trigonometric identities.

Answer 1

sin theta =3/5
P=3
H=5
B=root H^2-P^2
B=root5^2-3^2
B=root25-9
B=root 16
B=4
cos=4/5
tan=3/4
cosec=5/3
sec=5/4
cot=4/3

I hope it will help you

Answer 2

Given,

sin θ = 3/5

To find,

The values of other trigonometric identities.

Solution,

• sin θ = 3/5.

We know that cos²θ = 1-sin²θ

⇒   cos²θ= 1-(3/5)²

⇒   cos²θ = 1 - (9/25)

⇒   cos²θ = (25-9)/25

⇒   cos²θ = 16/25.

• cos θ = 4/5.

⇒    tan  θ = (sin  θ)/ (cos  θ)

⇒   tan  θ = (3/5) / (4/5)

• tan  θ = 3/4.

• cosec  θ is reciprocal of sin θ , therefore cosec  θ = 5/3.

• sec  θ is reciprocal of cos θ , therefore sec  θ = 5/4.

• cot  θ is reciprocal of tan θ , therefore tan  θ = 4/3.

Hence,  sin θ = 3/5, cos θ = 4/5, tan  θ = 3/4, cosec  θ = 5/3,  sec  θ = 5/4, tan  θ = 4/3.