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Question

Which of the following statements is true for θ ranging from 0 to 90?


  1. cosθ,cotθ and cosecθ increases as θ increases.

  2. sinθ=cosθ for all the values of θ

  3. Trigonometric ratios values do not follow any pattern.

  4. sinθ,tanθ and secθ increases as θ increases.


Solution

The correct option is D

sinθ,tanθ and secθ increases as θ increases.


When θ=0,sin θ=0,cos θ=1 and tan θ=0.

When θ=30,sin θ=12,cos θ=32 and tan θ=13.

When θ=45,sin θ=12,cos θ=12 and tan θ=1

When θ=60,sin θ=32,cos θ=12 and tan θ=3.

From the above data, it is observed that as the value of θ increases, the values of sin θ and tan θ increases and the value of cos θ decreases.
We know that sec θ=1cos θ.Thus, the value of sec θ increases, as the value of cos θ decreases.

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