Question

Cos(-1) of -θ is negative or positive?

a. Negative
b. Positive
c. Both
d. None of the above

Answer 1

The cosine of the inverse of -θ, or cos(-1)(-θ), is positive (Option b).

Step-by-step explanation:

The cosine of the inverse of -θ, denoted as cos(-1)(-θ), refers to the angle whose cosine is -θ. In trigonometry, the cosine function is positive in the first and fourth quadrants of the unit circle. When considering the cosine of an angle in the fourth quadrant, the value is positive. Therefore, cos(-1)(-θ) is positive (Option b).

To illustrate, imagine an angle -θ in the fourth quadrant of the unit circle. The cosine of this angle, represented as cos(-θ), is the x-coordinate of the corresponding point on the unit circle. In the fourth quadrant, the x-coordinate is positive, leading to a positive value for cos(-θ).

In conclusion, the correct answer is b. Positive. Understanding the behavior of the cosine function in different quadrants is key to determining the sign of cos(-1)(-θ). In this context, the positive nature of the cosine function in the fourth quadrant establishes that cos(-1)(-θ) is positive.