Question

Solve the following equation for \( 0^{\circ}
Ask by Dawson Ross. in South Africa
Mar 12,2025

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Answer

The solutions for the equations are: 1. \(x = \arccos\left(\frac{1}{3}\right)\) 2. \(x = \arccot\left(\frac{15}{4}\right) + 20^{\circ}\) These solutions are valid within the range \(0^{\circ} < x < 90^{\circ}\).

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Extra Insights

To solve the equations, let's tackle them one at a time: **6.3.1:** The given equation is: \[ 3 \cos x - 2 = -1 \] First, we add 2 to both sides: \[ 3 \cos x = 1 \] Now, divide both sides by 3: \[ \cos x = \frac{1}{3} \] Next, we find \( x \) by taking the arccosine of \( \frac{1}{3} \): \[ x = \cos^{-1}\left(\frac{1}{3}\right) \] Using a calculator, we find: \[ x \approx 70.53^{\circ} \] So, the solution in the given range \( 0^{\circ}

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