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dodsonh16
01.09.2019 •
Mathematics
Can you rewrite a sine as a cosine function and vice versa when describing a general sinusoidal graph? explain.
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Ответ:
Step-by-step explanation:
* Lets explain how to solve the problem
- We can write a sine as a cosine by translate the sine function to the
left by![\frac{\pi}{2}](/tpl/images/0217/0401/0f5d0.png)
-![sin(x+\frac{\pi}{2})=cos(x)](/tpl/images/0217/0401/f11bd.png)
∵ The value of sin(0 + π/2) = 1
∵ cos(0) = 1
∴ sin(0 + π/2) = cos(0)
∴ If sin(x) translated to the left by
, then it will be
cos(x)
∴![sin(x+\frac{\pi}{2})=cos(x)](/tpl/images/0217/0401/f11bd.png)
- Vice versa
- We can write a cosine as a sine by translate the cosine function to
the right by![\frac{\pi}{2}](/tpl/images/0217/0401/0f5d0.png)
-![cos(x-\frac{\pi}{2})=sin(x)](/tpl/images/0217/0401/172e7.png)
∵ The value of cos(0 - π/2) = 0
∵ sin(0) = 0
∴ cos(0 - π/2) = sin(0)
∴ If cos(x) translated to the right by
, then it will be
sin(x)
∴![cos(x-\frac{\pi}{2})=sin(x))](/tpl/images/0217/0401/84c71.png)
- Look to the attached graphs for more understand
Ответ:
23/8*3=69/8
CHECK MY ANSWERS IN CASE I MADE A MISTAKE