The graph of y = –3sin (2x) is shifted to the left by 30° units and up 5 units. Write the new equation.
My answer y= -3sin (2x- 30°) +5
Is this correct?
no, make sure you adjust the coefficient which controls the period
You will need
y = –3sin (2(x + 15°)) + 5 , notice also that + moves it to the left, - to the right.
so the answer would be y= -3sin (2x + 30°) +5?
sorry, my error, I was too focused on the 15
your answer will be
y = –3sin (2(x + 30°)) + 5
or
y = –3sin (2x + 60°) + 5
see the graphs here:
https://www.wolframalpha.com/input/?i=plot+y+%3D+%E2%80%933sin+(2x),+y+%3D+%E2%80%933sin+(2x+%2B+%CF%80%2F3)+%2B+5
notice I changed the 60° to π/3 radians
Yes, your answer is correct. To shift the graph of y = -3sin(2x) to the left by 30° units, we need to subtract 30° from the angle inside the sine function. Therefore, the new equation becomes y = -3sin(2x - 30°).
To shift the graph up by 5 units, we add 5 to the entire function. So, the final equation is y = -3sin(2x - 30°) + 5. Well done!