Question

Express as a function of a DIFFERENT angle, 0, degrees, ≤, θ, is less than, 360, degrees0 ∘ ≤θ<360 ∘ . cosine, left bracket, 271, degrees, right bracket cos(271 ∘ )

Answer 1

To express cos(271°) as a function of a different angle, we can use the symmetry of the cosine function to find that cos(271°) is equivalent to cos(89°).

Step-by-step explanation:

The student has asked to express cos(271°) as a function of a different angle within the range 0° ≤ θ < 360°. Since the cosine function has a period of 360°, we can find an equivalent angle within one cycle (0° to 360°) by subtracting multiples of 360°. However, there's a quicker method, knowing that cosine is a periodic and even function, which allows us to use the symmetry of the cosine function about the y-axis. Specifically, because 271° is in the fourth quadrant, we can find an equivalent angle in the first quadrant, which is 360° - 271° = 89°. Therefore, cos(271°) = cos(89°).