Question

Sec 855$^{\circ}$ =}

• A. 1
• B. $\sqrt{2}$
• C. $-\sqrt{2}$
• D. -1

Hint:

Subtract $360^{\circ}$ repeatedly until the angle is between $0^{\circ}$ and $360^{\circ}$ to find the reference angle.

Answer 1

The Correct Option is C

Step 1: Concept
Trigonometric functions of large angles can be simplified by removing multiples of $360^{\circ}$.

Step 2: Meaning
$855^{\circ}$ can be written as $2 \times 360^{\circ} + 135^{\circ}$. Therefore, $\sec 855^{\circ} = \sec 135^{\circ}$.

Step 3: Analysis
$\sec 135^{\circ} = \sec(180^{\circ} - 45^{\circ})$. Since secant is negative in the second quadrant, this equals $-\sec 45^{\circ}$.

Step 4: Conclusion
Since $\sec 45^{\circ} = \sqrt{2}$, the value is $-\sqrt{2}$. Final Answer: (C)