Question
Solve the following equation for \( 0^{\circ}
Ask by Dawson Ross. in South Africa
Mar 12,2025
Ask by Dawson Ross. in South Africa
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
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 \(0^{\circ} < x < 90^{\circ}\).
Solution

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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}