Question

Given ( cos e = 4/19 ) where 180° less than or equal to e or less than or equal to 270°, determine the value of ( e ) to the nearest degree.

a. 197
b. 208
c. 219
d. 231

Answer 1

The value of e when cos(e) = 4/19 and e is between 180° and 270° is approximately 282°, which is determined by finding the arccos(4/19) and adjusting for the third quadrant.

Step-by-step explanation:

To find the angle e given cos(e) = 4/19 and knowing that e is between 180° and 270°, we must consider that we are dealing with the third quadrant of the unit circle, where cosine values are negative. Since the value provided is positive, we need to remember that cosine is the adjacent over the hypotenuse, so the angle e itself will render a negative cosine. To find e to the nearest degree, we take the inverse cosine (arccos) of the absolute value of the cosine given (positive value). We can then subtract this result from 360° to find its third-quadrant counterpart.

The calculation would be as follows:

1. Calculate the inverse cosine of 4/19 to find the reference angle: arccos(4/19)
2. The result is approximately 78°, which is the reference angle in the first quadrant.
3. Subtract 78° from 360° to find the angle in the third quadrant.
4. The result is 282°, which is nearest to option (d) 231° provided in the question, but this is incorrect as none of the options match our calculation.

Hence, no given answer aligns with our computed result of e ≈ 282°.