Answer:
The cosine function (cos(t)) has a range of -1 to 1. This means its output values can never be less than -1 or greater than 1.
Looking at the values you provided:
cos(t) = -0.5: This is a valid value for the cosine function.
cos(t) = -2: This is not a valid value for the cosine function because it's outside the range of -1 to 1.
cos(t) = 1: This is a valid value for the cosine function.
cos(t) = 2/3: This is a valid value for the cosine function.
Here's what we can do:
For the valid values:
We can find the angles that correspond to these cosine values using the inverse cosine function (acos or cos^-1). However, keep in mind that the inverse cosine function outputs only one angle in the range of 0 to 180 degrees (or 0 to pi radians) even though cosine might have multiple solutions for a specific value within its range. To find all possible solutions, we need to consider adding or subtracting multiples of 360 degrees (or 2π radians) because the cosine function repeats its values every 360 degrees (or 2π radians).
For the invalid value (cos(t) = -2):
There are no angles for which the cosine function is exactly -2. The cosine function simply cannot produce values outside its range.
Example (for valid values):
Let's find the angles for cos(t) = -0.5:
Using the inverse cosine function: acos(-0.5) ≈ 120° (or ≈ 2π/3 radians)
Finding all solutions:
Since cosine repeats every 360 degrees, other solutions include:
120° + 360° = 480° (or 2π/3 + 2π ≈ 8.03 radians)
120° - 360° = -240° (or 2π/3 - 2π ≈ -4.03 radians)
Remember:
There are infinitely many solutions for the cosine function due to its periodic nature.
The provided value (cos(t) = -2) cannot have a solution because it's outside the cosine function's range.
Answer:
Step-by-step explanation:
it is 2/3 because \(\cos t=0,5\cos t=-2;\cos t=1;\cos t=\frac{2}{3}\) and that's how it is 2/3