Solve 20cos θ + 11 = 0

June 8, 2026Mathematics

ScanSolve AI Answer

June 8, 2026

Answer

$\theta = 2n\pi \pm \arccos\left(-\frac{11}{20}\right), \quad where n \in \mathbb{Z}$

Step 1: Isolate the $\cos \theta$ term. The given equation is: $20 \cos \theta + 11 = 0$ Subtract 11 from both sides of the equation: $20 \cos \theta = -11$

Step 2: Solve for $\cos \theta$ . Divide both sides by 20: $\cos \theta = -\frac{11}{20}$

Step 3: Find the general solution for $\theta$ . To find $\theta$ , we take the inverse cosine of $-\frac{11}{20}$ . Let $\alpha = \arccos\left(-\frac{11}{20}\right)$ . The general solutions for $\cos \theta = k$ are given by: $\theta = 2n\pi \pm \alpha$ where $n$ is an integer.

Substituting $\alpha = \arccos\left(-\frac{11}{20}\right)$ : $\boxed{\theta = 2n\pi \pm \arccos\left(-\frac{11}{20}\right), \quad where n \in \mathbb{Z}}$ What's next?

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Quick Answer

Isolate the term. The given equation is: 20 + 11 = 0 Subtract 11 from both sides of the equation: 20 = -11 Step 2: Solve for .

Asked on June 8, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on June 8, 2026

Step 1: Isolate the term. The given equation is: 20 + 11 = 0 Subtract 11 from both sides of the equation: 20 = -11 Step 2: Solve for . Divide both sides by 20: = -(11)/(20) Step 3: Find the general solution for . To find , we take the inverse cosine of -(11)/(20). Let = (-(11)/(20)). The general solutions for = k are given by: = 2n ± where n is an integer. Substituting = (-(11)/(20)): = 2n ± (-(11)/(20)), where n Z What's next?