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Question

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

A

cosθ,cotθ and cosecθ increases as θ increases.

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B

sinθ,tanθ and secθ increases as θ increases.

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C

Trigonometric ratios values do not follow any pattern.

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D

sinθ=cosθ for all the values of θ

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Solution

## The correct option is B 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=1√3. When θ=45∘,sin θ=1√2,cos θ=1√2 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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