WEBVTT
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Convert the following angle measures from radians to degrees.
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Give your answers correct to the nearest degree where necessary.
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π over three radians, π over seven radians, and three π over eight radians.
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Letβs recall what we already know about radians.
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One full turn is equal to both 360 degrees and two π radians.
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Halving this gives us π radians equals 180 degrees.
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Letβs take this relationship further.
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Dividing both sides by π will give us the value of one radian.
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180 over π degrees is therefore equal to one radian.
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So to change radians into degrees, we can simply multiply by 180 over π.
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Letβs see how this helps us.
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Multiplying by 180 over π in our first example gives us π over three times 180 over π.
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Did you notice that thereβs a common factor of π?
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We can therefore cancel this through, leaving us with a third times 180 over one.
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Multiplying as normal gives us 180 over three or 60 degrees.
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π over three radians is therefore equal to 60 degrees.
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Now, consider our second example.
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Once again, we can multiply by 180 over π to convert our radians into degrees.
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Just like in the last example, we have a common factor of π.
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We can therefore divide through by π to leave us with a seventh times 180 over one.
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Multiplying here gives us 180 over seven, which doesnβt give us such a nice number.
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However, the question told us to give our answers correct to the nearest degree.
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180 divided by seven is 25.714 and so on.
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This gives us 26 degrees correct to the nearest degree.
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π over seven radians is therefore equal to 26 degrees correct to the nearest degree.
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At this point, you may wish to pause the video and give the final example a go yourself.
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Just like in the two previous examples, we are gonna start by multiplying by 180 over π.
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Once again, we can divide through by this common factor of π.
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This leaves us with three-eighths times 180 over one.
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Three-eighths times 180 over one is equal to 67.5.
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Correct to the nearest degree, this is 68 degrees.
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Three π over eight radians is therefore equal to 68 degrees correct to the nearest degree.