Question

\((\frac{2}{5}\cos 0^{\circ} - \frac{1}{5}\sin 0^{\circ})\) is equal to :

• A. \(\frac{1}{5}\)
• B. \(-\frac{2}{5}\)
• C. \(\frac{2}{5}\)
• D. \(\frac{3}{5}\)

Hint:

Since \(\sin 0^{\circ} = 0\), the entire second term disappears immediately.
You only need to evaluate \(\frac{2}{5} \times \cos 0^{\circ} = \frac{2}{5} \times 1 = \frac{2}{5}\).
This simplifies the problem to a single-step calculation.

Answer 1

The Correct Option is C

Step 1: Picture the angle instead of just recalling the values.
As an angle in a right triangle shrinks toward $0^\circ$, the side opposite it shrinks toward zero while the adjacent side grows to nearly equal the hypotenuse. This gives $\sin 0^\circ = 0$ and $\cos 0^\circ = 1$ directly, without needing to memorise a table.
Step 2: Substitute these into the expression.
\[ \frac{2}{5}\cos 0^\circ - \frac{1}{5}\sin 0^\circ = \frac{2}{5}(1) - \frac{1}{5}(0) \]
Step 3: Simplify.
\[ = \frac{2}{5} - 0 = \frac{2}{5} \]
Step 4: State the result.
So the value of the expression is $\frac{2}{5}$.
\[ \boxed{\dfrac{2}{5}} \]