Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Mar 05, 2024

Determine if $x=\pi/6$ is a solution to the equation $\cos x = \sqrt{3}/2$ using substitution.

STEP 1

Assumptions
1. We are given the equation $\cos x = \frac{\sqrt{3}}{2}$ .
2. We are asked to verify if $x = \frac{\pi}{6}$ is a solution to the equation.
3. We will use the substitution method to determine if the given $x$ -value satisfies the equation.

STEP 2

Substitute the given $x$ -value into the equation to check if the left-hand side (LHS) equals the right-hand side (RHS).
$\cos\left(\frac{\pi}{6}\right) \stackrel{?}{=} \frac{\sqrt{3}}{2}$

STEP 3

Evaluate the cosine of $\frac{\pi}{6}$ using the unit circle or trigonometric identities.
$\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$

STEP 4

Compare the result of the cosine function with the RHS of the original equation.
Since $\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$ and this matches the RHS of the equation $\frac{\sqrt{3}}{2}$ , we conclude that the given $x$ -value is indeed a solution to the equation.
$x = \frac{\pi}{6}$ is a solution to the equation $\cos x = \frac{\sqrt{3}}{2}$ .

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