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If sine x equals cosine x, what is x in radian?

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Squares And Square Roots Quiz - Examsegg Mathematics Aptitude

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If sine x equals cosine x, what is x in radian?

A. π/4

B. π/2

 C. π/3

D. π/12

QUICK ANSWER…

A

DETAILS…

Here, we are required to find the value of x so that sin x is the same as cos x.

Now we know that sin 45 is the same thing as cos 45 = 1/√2

Also, we know that π = 180°, therefore, 45° = 180/4 = π/4

This is the quickest solution, however, there’s a longer solution:

sin x = cos x

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sin²x = cos²x

but recall that cos²x + sin²x = 1

substituting cos²x for sin²x, we have:

sin²x + sin²x = 1

2sin²x = 1

sin²x = ½

sin x = √½ = 1/√2

x = sin¯¹ 1/√2 = 45° = π/4

Now for the right answer to the above question:

  1. Option A is correct.
  2. Option B is incorrect.
  3. C is incorrect.
  4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

  • Cos 45° = sin 45°
  • 180° = π
  • 45° = π/4
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/ culled from 2020 JAMB-UTME mathematics past question 10 /

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