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Difficulty: EasyTrigonometric Graphs and Simple Equations

Find the acute angle θ\theta, in degrees, that satisfies the trigonometric equation 3tan⁡θ−3=0\sqrt{3}\tan \theta - 3 = 0.

Answer: 60 degrees

Answer

The acute angle θ\theta is 60∘60^\circ.
Rearranging the equation 3tan⁡θ−3=0\sqrt{3}\tan \theta - 3 = 0 gives 3tan⁡θ=3\sqrt{3}\tan \theta = 3, so tan⁡θ=33=3\tan \theta = \frac{3}{\sqrt{3}} = \sqrt{3}. For an acute angle (0∘<θ<90∘0^\circ < \theta < 90^\circ), the angle with a tangent equal to 3\sqrt{3} is 60∘60^\circ.

Step-by-Step Solution

1
Isolate the trigonometric ratio tan⁡θ\tan \theta
tan⁡θ=3\tan \theta = \sqrt{3}
Add 33 to both sides and divide by 3\sqrt{3}, giving 33=3\frac{3}{\sqrt{3}} = \sqrt{3}.
2
Determine the value of the acute angle θ\theta
θ=60∘\theta = 60^\circ
From special angle exact values, tan⁡(60∘)=3\tan(60^\circ) = \sqrt{3}.

Key Concept

Solving Simple Trigonometric Equations
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Topics

Trigonometric Graphs and Simple Equations

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