Question

"( cos(θ) = {8}{9} ) must be between 0 and 360.

a) There is no solution within the given range.
b) ( θ = 28.07^° )
c) ( θ = 32.76^° )
d) ( θ = 61.93^° )

Answer 1

The approximate value of the angle θ that satisfies the equation cos(θ) = 8/9 is given by option (c) ( θ = 32.76°).

Step-by-step explanation:

The equation cos(θ) = 8/9 represents the cosine of an angle θ that is equal to 8/9. To find the angle θ between 0 and 360 degrees that satisfies this equation, we can use the inverse cosine function (cos⁻¹) or the arccosine function. Taking the arccosine of both sides of the equation, we have:

θ = cos⁻¹(8/9)

Using a calculator, we can evaluate the inverse cosine of 8/9 to find the value of θ. The calculator will give us an approximate value for θ in degrees. From the given options, we can see that option (c) is the closest to the approximate value of θ obtained from the calculator.