CAT Practice : Trigonometry

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Number x lies between 0 and 1, higher powers of the number will be smaller than lower powers. Think about that. And then think about what does this have to do with Trigonometry.

Range of function

    Q.2: Sin2014x + Cos2014x = 1, x in the range of [-5π, 5π], how many values can x take?
    1. 0
    2. 10
    3. 21
    4. 11


  • Correct Answer
    Choice C. 21

Explanatory Answer

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Detailed Solution

We know that Sin2x + Cos2x = 1 for all values of x.
If Sin x or Cos x is equal to –1 or 1, then Sin2014x + Cos2014x will be equal to 1.

Sin x is equal to –1 or 1 when x = –4.5π or –3.5π or –2.5π or –1.5π or –0.5π or 0.5π or 1.5π or 2.5π or 3.5π or 4.5π.
Cosx is equal to –1 or 1 when x = –5π or –4π or –3π or –2π or –π or 0 or π or 2π or 3π or 4π or 5π.

For all other values of x, Sin2014 x will be strictly lesser than Sin2x.
For all other values of x, Cos2014 x will be strictly lesser than Cos2x.

We know that Sin2x + Cos2x is equal to 1. Hence, Sin2014x + Cos2014x will never be equal to 1 for all other values of x. Thus there are 21 values.
Answer choice (C)

Correct Answer: 21 Values

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