Questions: f(x) = 7/10 sin(3(x - 3π/4)) ?

Transcript text: $f(x)=\frac{7}{10} \sin \left(3\left(x-\frac{3 \pi}{4}\right)\right) ?$

Solution

Solution Steps

To evaluate the function $ f(x) = \frac{7}{10} \sin \left(3\left(x-\frac{3 \pi}{4}\right)\right) $ for a given value of $ x $, we need to:

Subtract $\frac{3 \pi}{4}$ from $ x $.
Multiply the result by 3.
Compute the sine of the resulting value.
Multiply the sine value by $\frac{7}{10}$.

Step 1: Substitute $ x = 1 $ into the function

Given the function $ f(x) = \frac{7}{10} \sin \left(3\left(x-\frac{3 \pi}{4}\right)\right) $, we substitute $ x = 1 $.

Step 2: Simplify the expression inside the sine function

First, calculate the expression inside the sine function: \[ 3 \left(1 - \frac{3 \pi}{4}\right) = 3 \left(1 - 2.3562\right) = 3 \left(-1.3562\right) = -4.068 \]

Step 3: Compute the sine of the resulting value

Next, compute the sine of $-4.068$: \[ \sin(-4.068) \approx 0.7998 \]

Step 4: Multiply by $\frac{7}{10}$

Finally, multiply the sine value by $\frac{7}{10}$: \[ f(1) = \frac{7}{10} \times 0.7998 \approx 0.5599 \]

Final Answer

$\boxed{f(1) = \frac{7}{10} \sin \left(3\left(1-\frac{3 \pi}{4}\right)\right)}$

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