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3 years ago

What is the general equation of a sine function with an amplitude of 6, a period of π/4 and a horizontal shift of π/2?

Mathematics

2 answers:

Anika [276]3 years ago

8 0

The formula for the general sin function is $y=Asin(bx+c)$ where b is the period and c is the phase shift. We are given a period of $\frac{ \pi }{4}$ and the formula to solve for b is $period= \frac{2 \pi }{b}$ . We set up to solve for b: $\frac{ \pi }{4} = \frac{2 \pi }{b}$ . Cross multiply to get $b \pi =8 \pi$ and b = 8. Now for the phase shift. The formula for that is -c/b, and since we already know b, and we have a phase shift value of pi/2, we solve for c: $\frac{ \pi }{2}= \frac{-c}{8}$ and $8 \pi =-2c$ . Therefore, $c=-4 \pi$ . Putting all that together into the equation with the A value of 6, we have $y=6sin(8x-4\pi)$ . Factoring out the 8 then, the final equation is $y=6sin(8(x- \frac{\pi}{2} ))$ , third choice down.

AnnyKZ [126]3 years ago

4 0

Answer:

Step-by-step explanation:

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And replacing we got:

$n = (\frac{2.326*1.7}{0.3})^2= 173.73$

And the value for n rounded up would be n = 174

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