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Trigonometric equationsTrigonometryHigh schoolabout 0:33

Solve cos(x) = 2: animated lesson

A narrated, step-by-step trigonometric equations video lesson with captions. Final answer: No real solution.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Solving an equation
$\cos\left( x\right) = 2$
2. Step by step
1. $\cos\left( x\right) = 2$
  Start with the equation
2. $f(x) = \cos\left( x\right)-2 = 0$
  Rewrite as f(x) = 0
3. f repeats every 2π; it never reaches 0 in one full period
3. The answer
$\text{No real solution}$
No real solution

Transcript

The problem. Here is the problem: cos(x) equals 2. A periodic equation in x.

Step by step. Start with the equation. Rewrite as f(x) equals 0. f repeats every 2pi; it never reaches 0 in one full period. A scan of one whole period (and of [−100, 100]) finds no crossing and no touching point, so it has no real solution.

The answer. So the answer is No real solution. Because the function repeats, checking one full period covers every real number.

About trigonometric equations

Solve trigonometric equations and give every solution.

Solve cos(x) = 2: Animated Step-by-Step Lesson (High school)