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Given that the area of a circular sector is one-fourth of the area of a circle, find in radians the central angle, correct to one decimal place.
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We have a circle, and our circular sector is one-fourth of the area of the total circle.
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One-fourth of a circle would look like this.
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And the central angle of this sector is what is shown in pink, here.
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Itβs one-fourth of a turn, from zero degrees to 90 degrees.
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Itβs pretty recognisable.
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This is 90 degrees.
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But what is 90 degrees in radians?
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To find out, we take our degrees and we multiply it by π over 180 degrees.
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That gives us π over two.
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90 degrees is equal to π over two radians.
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We want to round this to one decimal place.
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If we divide π by two, we get an irrational number, 1.5707, and it continues without terminating.
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Rounding that to one decimal place, we look to the right of the tenths place; there is a seven.
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Weβre going to round the tenths place up to six, and then everything to the left of the six stays the same, one and six-tenths.
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90 degrees, a 25 percent turn in our circle, is about one and six-tenths radians.