Evaluate the trigonometric expression \tan 60^\circ \times \sin 60^\circ. What is the exac… — JAMB UTME

Evaluate the trigonometric expression $\tan 60^\circ \times \sin 60^\circ$ . What is the exact simplified value of the expression?

The exact simplified value of the expression is

\frac{3}{2}

Substituting the exact surd values of the special angles yields

\tan 60^\circ = \sqrt{3}

and

\sin 60^\circ = \frac{\sqrt{3}}{2}

. Multiplying these gives

\sqrt{3} \times \frac{\sqrt{3}}{2} = \frac{3}{2}

, which is the correct exact value.

Identify the values of the special trigonometric angles.

\tan 60^\circ = \sqrt{3}

and

\sin 60^\circ = \frac{\sqrt{3}}{2}

Special angle values must be known in exact surd form.

Multiply the two trigonometric ratios together.

\tan 60^\circ \times \sin 60^\circ = \sqrt{3} \times \frac{\sqrt{3}}{2} = \frac{(\sqrt{3} \times \sqrt{3})}{2}

Substitute the special angle values into the product expression.

Simplify the radical expression in the numerator.

\frac{3}{2}

The product of

\sqrt{3} \times \sqrt{3}

equals

3

Evaluation of Special Angle Trigonometric Values

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