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Question

# Which of the following statements is/are 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. Observe that as the value of θ increases, the values of sin θ and tan θ increase 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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