Li Fitzgerald
11/03/2023 · Elementary School
\( f ( x ) = 5 \sin x + 2 \cos x - 3 , a = \frac { 13 \pi } { 2 } \)
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Step-by-step Solution
Given the function \( f(x) = 5 \sin x + 2 \cos x - 3 \) and the value of \( a = \frac{13\pi}{2} \), we need to find the value of \( f(a) \).
To find \( f(a) \), we substitute the value of \( a \) into the function \( f(x) \) and evaluate it.
Substitute \( a = \frac{13\pi}{2} \) into the function \( f(x) \):
\[ f\left(\frac{13\pi}{2}\right) = 5 \sin\left(\frac{13\pi}{2}\right) + 2 \cos\left(\frac{13\pi}{2}\right) - 3 \]
Now, we can calculate the value of \( f\left(\frac{13\pi}{2}\right) \) by evaluating the trigonometric functions at \( \frac{13\pi}{2} \).
Calculate the value by following steps:
- step0: Calculate:
\(5\sin\left(\frac{13\pi }{2}\right)+2\cos\left(\frac{13\pi }{2}\right)-3\)
- step1: Calculate:
\(5\times 1+2\cos\left(\frac{13\pi }{2}\right)-3\)
- step2: Calculate:
\(5\times 1+2\times 0-3\)
- step3: Multiply the numbers:
\(5\times 1+0-3\)
- step4: Multiply:
\(5+0-3\)
- step5: Remove 0:
\(5-3\)
- step6: Subtract the numbers:
\(2\)
The value of \( f\left(\frac{13\pi}{2}\right) \) is 2.
Quick Answer
The value of \( f\left(\frac{13\pi}{2}\right) \) is 2.
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