For your first question, simply let x = 135, set your calculator to DEG
and let your device do the work for you. Notice 135-45 = 90° and you should know sin 90° without a calculator.
I will do the 2nd question:
if y = 15
15 = 10sin(x-45) + 20
-1/2 = sin(x-45)
from basic trig you know sin 210° = -1/2 or sin 330° = -1/2
so x-45 = 210 or x-45 = 330
x = 255°, or x = 375°
there are other answer: since the period of sin(x-45°) is 360°
more answers can be obtained by adding or subtracting 360 to any answer
other answers:
we have 375-360 = 15° <----- that would be our smallest positive answers.
3rd part:
if moved down 5 units, our new equation is y = 10sin(x-45°) + 15
so now
15 = 10sin(x-45) + 15
you try it.
A point on a wheel has an equation y = 10 sin (x - 45°) + 20 that models the height as the wheel rotates. Answer the following questions.
What is the height if the wheel has rotated 135°?
What are the possible values of rotation (i.e., the value of x) if the height is 15m?
If the hub of the wheel were moved down 5m, what would the values of rotation (the values of x) be if the height were 15m?
1 answer