Find all solutions to the equation. cos x = 1 \cos x=1 cos x = 1

this problem, we're asked to find all of the solutions to the equation the cosine of x is equal to 1. Now don't let this x throw you off because you may be confusing an x instead of a theta, but we are still doing the same thing. We're still looking for an angle for which the cosine is equal to 1. So the first thing we want to do is come over to our unit circle and find all of the angles for which the cosine is 1. Now there's actually only one angle for which this is true, and that's 0. The cosine of 0 is equal to 1, so that gives me my angle angle on my unit circle. So I have that x is equal to 0. But now that we have all of the values on our unit circle, we wanna take those, and we wanna add 2 pi into them. Now 0+2 pi n is really just 2 pi n. So I could most accurately represent represent my answer in its most simplified form as x is equal to 2 pi n. And that represents all of the solutions to the equation, the cosine of x is equal to 1. Thanks for watching, and let me know if you have any questions.

Find all solutions to the equation. cos ⁡ x = 1 \cos x=1 cos x = 1

x = π + 2 π n x=\pi+2\pi n x = π + 2 πn

x = π 2 + 2 π n , x = 3 π 2 + 2 π n x=\frac{\pi}{2}+2\pi n,x=\frac{3\pi}{2}+2\pi n x = 2 π + 2 πn , x = 2 3 π + 2 πn

11. Inverse Trigonometric Functions and Basic Trig Equations

Linear Trigonometric Equations

Precalculus

11. Inverse Trigonometric Functions and Basic Trig Equations

Linear Trigonometric Equations

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Multiple Choice

Find all solutions to the equation.
$\cos x=1$

$x=0$

$x=2\pi n$

$x=\pi+2\pi n$

$x=\frac{\pi}{2}+2\pi n,x=\frac{3\pi}{2}+2\pi n$

Verified step by step guidance

Start by understanding the equation cos(x) = 1. The cosine function equals 1 at specific points on the unit circle.

Recall that the cosine function has a period of 2π, meaning it repeats its values every 2π radians.

The primary angle where cos(x) = 1 is at x = 0. Since the cosine function is periodic, the general solution for cos(x) = 1 is x = 2πn, where n is an integer.

Consider other angles where the cosine function might equal 1. However, for cosine, the only angle in the interval [0, 2π) where cos(x) = 1 is x = 0.

Thus, the complete set of solutions for the equation cos(x) = 1 is given by x = 2πn, where n is any integer, representing the periodic nature of the cosine function.