For y=3 +7 cos 5 (theta - 28 degrees)
Find y when theta=321 degrees
To find the value of y when theta is equal to 321 degrees, we can substitute the given value of theta into the equation y = 3 + 7 cos 5(theta - 28 degrees).
First, let's convert 321 degrees to radians. Since there are π radians in 180 degrees, we can use the conversion factor:
321 degrees * π/180 ≈ 5.61 radians
Now, we substitute this value into the equation:
y = 3 + 7 cos 5(5.61 - 28 degrees)
Now we need to calculate cos(5(5.61 - 28 degrees)).
To do this, we first convert 28 degrees to radians:
28 degrees * π/180 ≈ 0.49 radians
Now we can substitute this value into the equation:
y = 3 + 7 cos 5(5.61 - 0.49)
Now simplify the expression inside the cosine function:
5(5.61 - 0.49) = 5(5.12) = 25.6
Substituting this back into the equation:
y = 3 + 7 cos 25.6
Finally, evaluate the cosine function:
cos(25.6) ≈ -0.827 (rounded to three decimal places)
Substituting this back into the equation:
y = 3 + 7(-0.827) = 3 - 5.789 = -2.789
Therefore, when theta is equal to 321 degrees, y is approximately -2.789.