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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
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:
- Option A is correct.
- Option B is incorrect.
- C is incorrect.
- 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 /
