If $$3+isin$$θ$$4$$−icosθ,θ∈$$0$$,$$2$$π , is a real number, then an argument of $$sin$$θ$$+icos$$θ is:

Correct option is 3π−tan−143

Questions

If $\frac{3 + i \sin θ}{4 - i \cos θ}, θ \in [0, 2 π]$ , is a real number, then an argument of $\sin θ + i \cos θ$ is:

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−tan−134

π−tan−134

π−tan−143

tan−143

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detailed solution

Correct option is C

z=3+isinθ4−icosθ×4+icosθ4+icosθas z is purely real ⇒3cosθ+4sinθ=0⇒tanθ=−34∴argsinθ+icosθ=π-tan−1cosθsinθ or -tan−1cosθsinθ =π-tan−143 or -tan−143

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If 3+isinθ4−icosθ,θ∈0,2π , is a real number, then an argument of sinθ+icosθ is:

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Ready to Test Your Skills?

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If $\frac{3 + i \sin θ}{4 - i \cos θ}, θ \in [0, 2 π]$ , is a real number, then an argument of $\sin θ + i \cos θ$ is: