What is the smallest positive angle \theta, in degrees, that satisfies the trigonometric e… — JAMB UTME

What is the smallest positive angle $\theta$ , in degrees, that satisfies the trigonometric equation $\sqrt{3}\tan(3\theta) = 3$ ?

Answer: 20 degrees

The smallest positive value of

\theta

20^\circ

Isolating

\tan(3\theta)

gives

\tan(3\theta) = \frac{3}{\sqrt{3}} = \sqrt{3}

. The principal acute angle whose tangent is

\sqrt{3}

60^\circ

. Equating

3\theta = 60^\circ

and solving for

\theta

yields

\theta = 20^\circ

Isolate the trigonometric function

\tan(3\theta)

\tan(3\theta) = \sqrt{3}

Dividing both sides by \sqrt{3} isolates the tangent term and rationalizes the fraction to \sqrt{3}.

Determine the principal angle for

3\theta

3\theta = 60^\circ

The smallest positive angle whose tangent equals \sqrt{3} is 60^\circ.

Solve for

\theta

\theta = 20^\circ

Dividing the principal angle 60^\circ by the coefficient 3 gives the smallest positive angle \theta.

Solving trigonometric equations with multiple angle arguments

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