What is the value of sec39∘ to the nearest thousandth?
3.750
1.589
1.287
0.629
on your calculator, make sure your setting is DEG
do:
1 ÷ cos39°
write down what you get.
In order to find the value of sec(39°) to the nearest thousandth, you can use a scientific calculator or mathematical software.
Here's a step-by-step explanation of how to do it:
1. Start by converting the angle from degrees to radians, since trigonometric functions often accept radians as input. The formula to convert from degrees to radians is:
radians = (π / 180) * degrees
For sec(39°), you would have:
radians = (π / 180) * 39 = 0.6807 radians (rounded to four decimal places)
2. Once you have the angle in radians, use the reciprocal of the cosine function to find sec(x). The formula for sec(x) is:
sec(x) = 1 / cos(x)
For sec(0.6807), you would have:
sec(39°) = 1 / cos(0.6807)
3. Use a calculator or mathematical software to find the cosine of 0.6807 radians, and then calculate the reciprocal:
cos(0.6807) ≈ 0.7683
sec(39°) = 1 / 0.7683 ≈ 1.3007
4. Finally, round the result to the nearest thousandth:
sec(39°) ≈ 1.301
Therefore, the value of sec(39°) to the nearest thousandth is approximately 1.301.
To find the value of sec39∘, we can use the trigonometric definition of secant:
secθ = 1 / cosθ
In this case, we want to find sec39∘. We can find the value of cos39∘ using a scientific calculator or trigonometric tables.
cos39∘ ≈ 0.766
Now, we can find the value of sec39∘:
sec39∘ ≈ 1 / 0.766 ≈ 1.304
Therefore, the value of sec39∘ to the nearest thousandth is 1.304.