Question

Use the given value to evaluate each function. cos(−t) = −5/9. What is the value of cos(t)?

a) 5/9
b) −5/9
c) 9/5
d) −9/5

Answer 1

The correct value of cos(t) when cos(-t) = -5/9 is 5/9, as the cosine function is even and cos(-t) = cos(t).

Step-by-step explanation:

The cosine function is an even function, which means it has symmetry about the y-axis. This attribute of the cosine function means that cos(-t) = cos(t). Therefore, if cos(-t) is given as -5/9, then the value of cos(t) is the same but without the negative sign, which makes it 5/9.

It is important to remember that the cosine of an angle does not change if we switch the angle from positive to negative, which is due to the periodic and even nature of the cosine function. Thus, no additional calculation is needed beyond understanding this property of trigonometric functions to find the direct answer to the problem.

The choice that matches this understanding is (a) 5/9.