WEBVTT
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Given that π₯ is an acute angle and four multiplied by the cos of π₯ equals two root three, determine the value of π₯ in radians.
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We are told that π₯ is an acute angle, which means it lies between zero and 90 degrees.
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However, in this question, we want our answer in radians.
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We recall that 180 degrees is equal to π radians.
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This means that 90 degrees is equal to π over two radians and π₯, therefore, lies between zero and π by two.
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We will begin to solve the equation in this question by making cos of π₯ the subject.
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We can do this by dividing both sides of the equation by four.
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The left-hand side simplifies to the cos of π₯.
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Dividing the numerator and denominator of the right-hand side by two gives us root three over two.
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The cos of π₯ equals root three over two.
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We can then solve this equation using our knowledge of the inverse trigonometric functions.
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We know that for any acute angle π, the inverse cos of cos π is equal to π.
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Taking the inverse cosine of both sides of our equation gives us the inverse cos of cos π₯ is equal to the inverse cos of root three over two.
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Since π₯ is an acute angle, we can therefore conclude that π₯ is equal to the inverse cos of root three over two.
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We can then type the right-hand side into our calculator.
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Ensuring that weβre in radian mode, we get an answer for π₯ of π over six.
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If π₯ is an acute angle and four multiplied by the cos of π₯ is two root three, then π₯ is equal to π over six radians.
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It is worth noticing here that we couldβve solved the final step of our equation using our knowledge of special angles.
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We recall that the cos of 30 degrees is equal to root three over two.
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This means that the cos of π over six radians is also equal to root three over two.
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Taking the inverse cosine of both sides of this equation, we see that π over six is equal to the inverse cos of root three over two.
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This confirms that we have the correct answer for π₯.