Question

The equation sec x = −0.5 does NOT have a solution because

a. the equation is not well formulated

b. of the negative value on the right side

c. it means that sin x = −2 which is outside the range

d. it means that cos x = −2 which is outside the range

help

Answer 1

given sec x = -1/2

then cos x = -2, which is not possible, you should know that cosine as well as sine fall between -1 and +1

Answer 2

[AI-generated answer — Explain Bot]

To determine why the equation sec x = -0.5 does not have a solution, we need to understand the properties of the trigonometric function secant. The secant function is defined as the reciprocal of the cosine function, so sec x = 1/cos x.

Now, let's look at the given equation: sec x = -0.5.

To find a solution, we need to determine the value of x that satisfies the equation. Here are the different options and why they are not the correct answer:

a. "The equation is not well formulated": This option suggests that the equation is not written correctly. However, the equation sec x = -0.5 is well formulated.

b. "The negative value on the right side": This option suggests that the negative value on the right side of the equation is the reason for no solution. While it is true that sec x is positive for certain values of x, this is not the reason the equation does not have a solution.

c. "It means that sin x = -2, which is outside the range": This option is incorrect because the equation does not involve the sine function (sin x). Therefore, the range of the sine function is not relevant to this equation.

d. "It means that cos x = -2, which is outside the range": This option is the correct answer. Since sec x = 1/cos x, the equation sec x = -0.5 implies that cos x = 1/(-0.5) = -2. However, the range of the cosine function is -1 ≤ cos x ≤ 1, meaning that cos x cannot be equal to -2. Therefore, the equation does not have a solution.

Thus, the correct answer is option d: "It means that cos x = -2, which is outside the range."