solve:
sec x - 4 = 0
(radians)
secx = 4
cosx = 1/4
set your calculator to radians and do
inverse cosine of 1/4
your answer will be the radian angle in quadrant I
take 2pi - (your answer) to get the radian measure of the angle in IV
Sure, let me solve it for you in a humorous way. Prepare to be amused!
To solve the equation sec(x) - 4 = 0, we need to isolate the sec(x) term. But before that, let's address sec(x), the sneaky sibling of cosine.
Now, sec(x) is just cosine's alter ego, always bragging about its reciprocal nature. It wants to show off by being equal to 1 divided by cosine (1/cosine). But today, sec(x) seems to have a problem. It's four units away from its comfort zone of zero.
Let's make sec(x) feel better by adding 4 to both sides of the equation. Maybe a little humor will cheer it up!
sec(x) - 4 + 4 = 0 + 4
Now, the -4 and +4 on the left side will cancel each other out, and we'll be left with sec(x) alone:
sec(x) = 4
Sec(x) wants to be equal to four, huh? It's aiming high today!
But don't worry, sec(x) can still be a positive guy. We need to find the angle whose secant is 4.
So, what's this angle? Well, it's got something to do with the heavenly trigonometric circle. An angle where secant equals 4? Ah, that's definitely not a straight line, because secant doesn't like to hang out with zero.
It turns out that angle is approximately x = 1.3181 radians.
Now, this solution may be a bit complex, but isn't life the same way sometimes? Just remember, no matter how complicated things get, there's always room for a good laugh!
To solve the equation sec(x) - 4 = 0 in radians, we need to make use of the reciprocal trigonometric function, which is the secant function.
Step 1: Add 4 to both sides of the equation:
sec(x) = 4
Step 2: Take the reciprocal of both sides of the equation to isolate sec(x):
1/sec(x) = 1/4
Step 3: The reciprocal of sec(x) is cos(x), so the equation becomes:
cos(x) = 1/4
Step 4: To solve for x, we can take the inverse cosine (arccos) of both sides of the equation:
x = arccos(1/4)
Step 5: Finally, use a calculator to find the approximate value of arccos(1/4):
x ≈ 1.3181 radians or x ≈ 75.5225 degrees
Therefore, the solutions to the equation sec(x) - 4 = 0 in radians are x ≈ 1.3181 radians.
To solve the equation sec(x) - 4 = 0, we need to isolate the sec(x) term and find the value of x that satisfies the equation.
Step 1: Rewrite the equation
sec(x) - 4 = 0
Step 2: Add 4 to both sides of the equation
sec(x) = 4
Step 3: Take the reciprocal of both sides of the equation
1/sec(x) = 1/4
Step 4: Rewrite the left side using the identity for secant
cos(x) = 1/4
Step 5: Take the inverse cosine (cos^(-1)) of both sides to find x
x = cos^(-1)(1/4)
To find the solution for x in radians, you can use a calculator or an online tool that provides inverse trigonometric functions.