Solve for $$ x $$, where $$ 0^{\circ} \leqslant x \leqslant 90^{\circ} $$ 1) $$ 5 \cos x=3 $$

Question

UpStudy AI · Accepted Answer

1) Given the equation

$$
5 \cos x = 3
$$

2) Divide both sides by 5 to isolate $$\cos x$$:

$$
\cos x = \frac{3}{5}
$$

3) To solve for $$ x $$, take the inverse cosine on both sides:

$$
x = \cos^{-1}\left(\frac{3}{5}\right)
$$

4) Since we are working in the domain $$0^{\circ} \leq x \leq 90^{\circ}$$, the solution is valid.

Thus, the solution for $$ x $$ is:

$$
x = \cos^{-1}\left(\frac{3}{5}\right)
$$

If an approximate value is needed, note that:

$$
x \approx 53.13^{\circ}
$$
$$ x = \cos^{-1}\left(\frac{3}{5}\right) $$ or approximately $$ 53.13^{\circ} $$.

Solve for \( x \), where \( 0^{\circ} \leqslant x \leqslant 90^{\circ} \) 1) \( 5 \cos x=3 \)