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Find the values of π in radians such that the function π of π equals tan of three π is undefined.
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To answer this question, we first need to consider the domain of the tangent function.
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The domain of the function π of π, which is equal to tan π, when working in radians is all real numbers except for π is equal to π over two plus ππ, where π is an integer.
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So thatβs π over two plus integer multiples of π.
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In other words, the tangent function is undefined when π is equal to any of these values, when π is equal to π over two plus any integer multiple of π.
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We should recall that these values of π correspond to the positions of the vertical asymptotes on the graph of tan π.
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However, in this question weβre working with the function π of π is equal to tan of three π.
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So to find where this function is undefined, we need to consider when three π is equal to any of these values.
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So weβre looking for when three π is equal to π over two plus ππ, where π is an integer.
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Dividing both sides of this equation by three, we find that π of π will be undefined when π is equal to π by six plus ππ over three.
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So weβve completed the problem.
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The function π of π which is equal to tan of three π is undefined when π is equal to π by six plus ππ over three, where π represents any integer.