Question
h) \( 2 \sec 60^{\circ} \)
Ask by Stanley Bright. in South Africa
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 2 \sec 60^{\circ} = 4 \)
Solution
1. Recall the definition of the secant function:
\[
\sec 60^{\circ} = \frac{1}{\cos 60^{\circ}}
\]
2. Evaluate \( \cos 60^{\circ} \):
\[
\cos 60^{\circ} = \frac{1}{2}
\]
3. Compute \( \sec 60^{\circ} \):
\[
\sec 60^{\circ} = \frac{1}{\frac{1}{2}} = 2
\]
4. Finally, multiply by 2:
\[
2 \sec 60^{\circ} = 2 \times 2 = 4
\]
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Simplify this solution The Deep Dive
Did you know that the secant function is the reciprocal of the cosine function? So, when you calculate \( \sec 60^{\circ} \), which equals \( \frac{1}{\cos 60^{\circ}} \), you get \( \frac{1}{0.5} = 2 \). Therefore, \( 2 \sec 60^{\circ} \) simply equals 4! If you're looking to apply this knowledge, consider the uses of secant in real-life applications. Secant is often found in engineering and physics, especially when analyzing wave functions and oscillations where angles play a critical role. Knowing your angles can elevate your understanding of these practical scenarios!
