Question

Difficulty: EasyBasic Trigonometric Ratios, Special Angles, and Identities

What is the numerical value of $4\sin 30^\circ + 2\cos 60^\circ - \tan 45^\circ$ ?

Answer: 2

Substituting the exact trigonometric values for special angles into the expression gives

4\left(\frac{1}{2}\right) + 2\left(\frac{1}{2}\right) - 1 = 2 + 1 - 1 = 2

Recall exact values for special trigonometric angles

\sin 30^\circ = \frac{1}{2}

\cos 60^\circ = \frac{1}{2}

, and

\tan 45^\circ = 1

These are standard special angle values derived from standard right-angled triangles.

Substitute the values into the original expression

4\left(\frac{1}{2}\right) + 2\left(\frac{1}{2}\right) - 1 = 2 + 1 - 1

Direct algebraic substitution.

Simplify the resulting numerical expression

Combining terms

2 + 1 - 1

gives

2

Basic Trigonometric Ratios and Special Angles

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