CAT questions from trigonometry.

1. Trigonometry

2. Trigonometry
Sin2014x + Cos2014x = 1, x in the range of [-5, 5], how many values
can x take?
(a) 0 (b) 10
(c) 21 (d) 11

3. Trigonometry
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.
Sin2014x + Cos2014x = 1, x in the range of [-5, 5], how many values
can x take?

4. Trigonometry
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)
Sin2014x + Cos2014x = 1, x in the range of [-5, 5], how many values
can x take?

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