Interactive Simulators

Interactive Equations Simulator

Explore how basic trigonometric equations like sin⁡(x)=C\sin(x) = C or cos⁡(x)=C\cos(x) = C intersect with specific values, revealing multiple solutions across different intervals.
π2π-π-2π0.17π0.83π-1.83π-1.17π

Showing solutions for sin(x) = 0.50 in the interval [-2π, 2π].

Trigonometric equations often have multiple solutions due to their periodic nature.

Solved Problems

Example

Problem 1: Solve 2cos⁡x−3=02 \cos x - \sqrt{3} = 0 for x∈[0,2π)x \in [0, 2\pi).

Step-by-Step Solution

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Example

Problem 2: Solve 2sin⁡2x−sin⁡x−1=02\sin^2 x - \sin x - 1 = 0 for x∈[0,2π)x \in [0, 2\pi).

Step-by-Step Solution

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Example

Problem 3: Solve 2cos⁡2x−1=02\cos^2 x - 1 = 0 for the general solution.

Step-by-Step Solution

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Example

Problem 4: Solve sin⁡(2x)=32\sin(2x) = \frac{\sqrt{3}}{2} for x∈[0,2π)x \in [0, 2\pi).

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