Question

How do you find the important points to graph `y = (1/2)sin(x - pi)`?

Answer 1

You can use the given trigonometric equation to compute for the rectangular coordinate points `(x, y)`, then use these points to draw your graph.

Explanation:

From the given equation
`y=1/2*sin(x-pi)`

Compute the rectangular coordinate points `(x, y)`

`x` in degrees and radians

`"degrees x y " " " " y in decimals"`
`" "0` `" "0` `" "0` `" "0`

`" "30` `" "pi/6` `" "-1/4` `" "-0.25`

`" "45` `" "pi/4` `" "(-sqrt2)/4` `" "-0.3535533906`

`" "60` `" "pi/3` `" "(-sqrt3)/4` `" "-0.4330127019`

`" "90` `" "pi/2` `" "-1/2` `" "-0.5`

`" "120` `" "(2pi)/3` `" "(-sqrt3)/4` `" "-0.4330127019`

`" "135` `" "(3pi)/4` `" "(-sqrt2)/4` `" "-0.3535533906`

`" "150` `" "(5pi)/6` `" "-1/4` `" "-0.25`

`" "180` `" "pi` `" "0` `" "0`

`" "210` `" "(7pi)/6` `" "1/4` `" "0.25`

`" "225` `" "(5pi)/4` `" "(sqrt2)/4` `" "0.3535533906`

`" "240` `" "(4pi)/3` `" "(sqrt3)/4` `" "0.4330127019`

`" "270` `" "(3pi)/2` `" "1/2` `" "0.5`

`" "300` `" "(5pi)/3` `" "(sqrt3)/4` `" "0.4330127019`

`" "315` `" "(7pi)/4` `" "(sqrt2)/4` `" "0.3535533906`

`" "330` `" "(11pi)/6` `" "1/4` `" "0.25`

`" "360` `" "2pi` `" "0` `" "0`

The draw your graph

graph{(y-1/2*sin(x-pi))=0[-5,5,-2.5,2.5]}

God bless....I hope the explanation is useful.