Final answer:
To find the exact value of cos(-π/3), we can use the unit circle. At -π/3 radians, the x-coordinate is negative in the second quadrant. Since cos(-π/3) = cos(π/3), the exact value is 1/2.
Step-by-step explanation:
To find the exact value of the trigonometric function cos(-π/3), we need to use the unit circle. The cosine function represents the x-coordinate of a point on the unit circle. At -π/3 radians, we can see that the cosine function is negative because the x-coordinate is negative in the second quadrant. Since the cosine of -π/3 is equal to the cosine of π/3 (the angles are coterminal), we can use the unit circle to find the exact value.
On the unit circle, at π/3 radians, the coordinates of the point on the circle are (1/2, √3/2). Since the cosine function represents the x-coordinate, the exact value of cos(π/3) is 1/2. Since cos(-π/3) = cos(π/3), the exact value of cos(-π/3) is also 1/2.