Which of the following has a positive value?tan(200°)sin(200°)sec(200°)cos(200°)

To determine which of the following has a positive value, we need to evaluate each trigonometric function separately.

1. tan(200°): To find the value of tan(200°), we can use the identity tan(x) = sin(x) / cos(x). Therefore, tan(200°) = sin(200°) / cos(200°).

2. sin(200°): To find the value of sin(200°), we can use the unit circle or a calculator. The sine function is positive in the second and third quadrants. Since 200° is in the third quadrant, sin(200°) is positive.

3. sec(200°): To find the value of sec(200°), we can use the identity sec(x) = 1 / cos(x). Therefore, sec(200°) = 1 / cos(200°).

4. cos(200°): To find the value of cos(200°), we can use the unit circle or a calculator. The cosine function is negative in the second and third quadrants. Since 200° is in the third quadrant, cos(200°) is negative.

Now, let's evaluate each expression:

tan(200°) = sin(200°) / cos(200°) = positive / negative = negative

sin(200°) = positive

sec(200°) = 1 / cos(200°) = 1 / negative = negative

cos(200°) = negative

From the given options, only sin(200°) has a positive value.