tanθ increases faster than sinθ as θ increases.

Question

Write ‘True’ or ‘False’ and justify your answer.

tanθ increases faster than sinθ as θ increases.

Answer 1

True

We know that sinθ increases as θ increases but cosθ decreases as θ increases. 

We have tan θ = sin θ/cos θ 

Now as θ increases, sinθ increases but cosθ decreases. Therefore, in case of tanθ, the numerator increases and the denominator decreases. But in case of sinθ which can be seen as sin θ/1, only the numerator increases but the denominator remains fixed at 1. 

Hence tanθ increases faster than sinθ as θ increases.