x=sec^-1 2
I really need help with this problem. Thanks
x= arcsec 2= arccos1/2=60deg
To solve for x in the equation x = sec^-1 2, we need to find the angle whose secant is equal to 2. Here's a step-by-step explanation of how to solve this problem:
Step 1: Understand the concept
The secant function (sec) is the reciprocal of the cosine function (cos). In other words, sec(theta) = 1 / cos(theta). The inverse secant function (sec^-1 or arcsec) gives us the angle whose secant value is equal to a given number.
Step 2: Find the angle whose secant is 2
Since we are looking for the angle whose secant is equal to 2, we can rewrite the equation as:
x = sec^-1 2
Step 3: Determine the potential values
The secant function takes on values between -∞ and -1, as well as between 1 and ∞. However, sec^-1 only returns angles between 0 and π (or 0 and 180°). Therefore, we are only interested in the positive range of sec^-1.
Step 4: Use a calculator or table
To find the angle whose secant is 2, we can use a scientific calculator or refer to a trigonometric table.
If you're using a scientific calculator, follow these steps:
- Press the "2nd" or "Shift" button (this allows you to access the inverse function)
- Look for the button labeled "sec^-1" or "arcsec"
- Enter "2" and calculate the result
If you're using a table, look for the row corresponding to sec^-1 and find the value closest to 2. The corresponding angle will be the solution.
Using either method, you will find that sec^-1 2 is approximately equal to 1.0472 radians (or 60°).
So the solution to the equation x = sec^-1 2 is x ≈ 1.0472 radians (or 60°).
I hope this explanation helps you understand the process of solving the problem. Let me know if you need any further assistance!