II. 14 Solve trigonometric equations I
COB
You

Find all solutions with . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

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Ask by Campbell Ingram. in Kuwait

Jan 22,2025

Question

II. 14 Solve trigonometric equations I
COB
You

Find all solutions with . Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

믐

Ask by Campbell Ingram. in Kuwait

Jan 22,2025

UpStudy AI · Accepted Answer

To solve the trigonometric equation:

$$
-10 \cos(\theta) - 5 = 0
$$

**Step 1: Isolate the cosine term**

$$
-10 \cos(\theta) = 5 \
\cos(\theta) = -\frac{5}{10} \
\cos(\theta) = -\frac{1}{2}
$$

**Step 2: Determine the angles where $$\cos(\theta) = -\frac{1}{2}$$ within the interval $$0 \leq \theta \leq \pi$$**

The cosine function equals $$-\frac{1}{2}$$ at:

$$
\theta = \frac{2\pi}{3}
$$

within the specified interval.

**Final Answer:**

$$
\theta = \frac{2\pi}{3}
$$
$$ \theta = \frac{2\pi}{3} $$