Question

Use a calculator to evaluate below function. Cos(110°54'21")

Answer 1

The value of cos(110°54'21") is approximately -0.342.

Step-by-step explanation:

To evaluate the function cos(110°54'21"), you can use a calculator that has trigonometric functions.

1. Convert the given angle from degrees, minutes, and seconds to decimal degrees:

- 1 degree = 60 minutes

- 1 minute = 60 seconds

To convert 54 minutes to degrees, divide it by 60:

54 minutes / 60 = 0.9 degrees

To convert 21 seconds to degrees, divide it by 3600 (60 seconds in a minute, and 60 minutes in a degree):

21 seconds / 3600 = 0.005833 degrees

Add the degrees, minutes, and seconds converted to degrees:

110 degrees + 0.9 degrees + 0.005833 degrees = 110.905833 degrees

2. Use a calculator to evaluate the cosine of the converted angle:

cos(110.905833 degrees) ≈ -0.342

Therefore, cos(110°54'21") is approximately -0.342.

Answer 2

Using a calculator, the value of cos(110 degrees, 54 minutes, 21 seconds) is approximately -0.4055.

Step-by-step explanation:

To find cos(110 degrees, 54 minutes, 21 seconds), convert the angle to decimal degrees. Since there are 60 minutes in a degree and 60 seconds in a minute, the conversion is:

`\[ 110^\circ54'21`

Calculating the decimal equivalent:

`\[ 110^\circ54'21`

Now, use a calculator to find the cosine of 110.9058 degrees. The cosine function represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle. In this case, it indicates the x-coordinate of a point on the unit circle.

`\[ \cos(110.9058^\circ) \approx -0.4055 \]`

The negative sign signifies that the angle 110.9058 degrees is in the second quadrant, where the cosine function is negative.

In conclusion, the calculation involves converting the angle to decimal degrees and using a calculator to find the cosine value. The result, approximately -0.4055, represents the cosine of 110.9058 degrees, providing insight into the angle's position on the unit circle. Understanding trigonometric functions and angle measures is crucial for accurate evaluations in various mathematical and scientific contexts.