Question

Express tan theta in terms of sin theta

Answer 1

tan x = sinx/cosx
= sinx/sin(90-x)

or

sinx/√(1-sin^2(x))

Answer 2

Tan θ in terms of sin θ is tan θ = sin θ/√(1- sin²θ)

Given problem:

Express tanθ in terms of sin θ  

To find:

tanθ in terms of sin θ  

Solution:

Condition used:

From trigonometric ratios

tan θ = sin θ/cos θ

From trigonometric identites

=> sin²θ + cos²θ = 1

=> cos θ = √(1- sin²θ)  

By using the above conditions we can

solve the given problem as shown below  

=> tan θ = sin θ/cos θ --- (1)

Substitute cos θ = √(1- sin²θ)  

=> tan θ = sin θ/√(1- sin²θ)  

Therefore,

Tan θ in terms of sin θ is tan θ = sin θ/√(1- sin²θ)

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