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What is the phase shift, vertical displacement with respect to #y=sinx# for the graph #y=sin(x-50^circ)+3#?

Answer 1

Zoe Austin

#"phase shift " =+50^@,"vertical shift" =+3#

The standard form of the #color(blue)"sine function"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))#

#"where amplitude " =|a|," period " =360^@/b#

#"phase shift " =-c/b" and vertical displacement " =d#

#" here " a =1,b=1,c=-50^@" and " d=+3#

#rArr"phase shift " =-(-50^@)/1=+50^@rarr" shift right"#

#"and vertical displacement " =+3uarr#

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Answer 2

Zoe Austin

The phase shift of the graph y = sin(x - 50°) + 3 with respect to y = sin(x) is 50° to the right. The vertical displacement is 3 units upwards.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.