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

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A. π/4

B. π/2

C. π/3

D. π/12

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

sin²x = cos²x

but recall that cos²x + sin²x = 1

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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…

• Cos 45° = sin 45°
• 180° = π
• 45° = π/4
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