SOLUTION: Hi, I'm really stuck on these two questions from trigonometry. Any chance I could get some help? Thanks in advance! https://drive.google.com/file/d/11VL_RMNxbHDdBnerDPi9ifWkRZIJ

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Question 1189886: Hi, I'm really stuck on these two questions from trigonometry. Any chance I could get some help? Thanks in advance!
https://drive.google.com/file/d/11VL_RMNxbHDdBnerDPi9ifWkRZIJDfMD/view?usp=sharing
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The general transformations for the sine function, y+=+sin%28theta%29, are:
y+=+a%2Asin%28b%28theta+-c%29%29+%2B+d
a+=> vertical dilation (stretch) of the amplitude
b => horizontal compression (shrink) of the period- defined as 2pi%2Fb
c => horizontal shift (left/right) The phase shift is defined as c%2Fb
d+=> vertical shift (up/down)



Equation........Amplitude........Period........HorizontalTranslation........Equation of Midline
y=sin%28x-3%29%2B1
Amplitude......1.
Period.........2pi%2F1+=2pi
Horizontal Translation.......3 (3 units right)
Equation of Midline.............................y=1

y+=+6sin+%280.25%28x%2B+45+%29%29-+9 ->45° =pi%2F4 radians
y+=+6sin%280.25%28x%2B+pi%2F4+%29%29-+9

Amplitude.......6
Period.......2pi%2F0.25=2pi%2F%281%2F4%29=8pi
Horizontal Translation......+C%2FB=45° or pi%2F4
Equation of Midline..........y=-9
y+=2sin%288%28x%2B+3%29%29%2B5
Amplitude.......2
Period.......2pi%2F8=pi%2F4
Horizontal Translation......C+%2F+B+=+3
Equation of Midline..........y=5

y+=0.75sin+%284%28x-+60+%29%29...............60° =pi%2F3radians
y+=0.75sin+%284%28x-+pi%2F3+%29%29
Amplitude.......0.75
Period.......2pi%2F4=pi%2F2
Horizontal Translation...... +C%2FB=60 or pi%2F3
Equation of Midline..........y=0