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: Understanding the Question:
This question is from Trigonometry, focusing on evaluating expressions containing specific standard angles.
We need to calculate the exact value of the given expression using the values of \(\cos 0^{\circ}\) and \(\sin 0^{\circ}\).

Step 2: Key Formula or Approach:
We utilize the standard values of basic trigonometric ratios:
\[ \cos 0^{\circ} = 1 \]
\[ \sin 0^{\circ} = 0 \]

Step 3: Detailed Explanation:
The given expression is:
\[ \frac{2}{5}\cos 0^{\circ} - \frac{1}{5}\sin 0^{\circ} \]
Substitute the known values \(\cos 0^{\circ} = 1\) and \(\sin 0^{\circ} = 0\) into the expression:
\[ = \frac{2}{5}(1) - \frac{1}{5}(0) \]
\[ = \frac{2}{5} - 0 \]
\[ = \frac{2}{5} \]

Step 4: Final Answer:
The value of the expression is \(\frac{2}{5}\).