If sin θ = 5/6, what are the values of cos θ and tan θ?

Solution:

It is given that

sin θ = 5/6

We know that

cos θ = √(1 - sin²θ)

Substituting the value of sin θ

cos θ = √(1 - (5/6)²)

cos θ = √(1 - 25/36)

cos θ = √11/36

cos θ = ±√11/6

From the trigonometric ratio

tan θ = sin θ/ cos θ 

Substituting the values

tan θ = 5/6/ ±√11/6

So we get

tan θ = 5/±√11

Therefore, the values of cos θ = ±√11/6 and tan θ = 5/±√11.

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If sin θ = 5/6, what are the values of cos θ and tan θ?

Summary:

If sin θ = 5/6, the values of cos θ = ±√11/6 and tan θ = 5/±√11.