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anemone
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Solve for $x$ such that $2\sin(x+30^\circ)\sin 16^\circ \sin 76^\circ=\sin 2028^\circ \sin 210^\circ$ for $0\lt x \lt 180^\circ$.
anemone said:Solve for $x$ such that $2\sin(x+30^\circ)\sin 16^\circ \sin 76^\circ=\sin 2028^\circ \sin 210^\circ$ for $0\lt x \lt 180^\circ$.
anemone said:Solve for $x$ such that $2\sin(x+30^\circ)\sin 16^\circ \sin 76^\circ=\sin 2028^\circ \sin 210^\circ$ for $0\lt x \lt 180^\circ$.
anemone said:Thanks both for participating and the solution...but...
Are you certain you haven't missed any solution? (Mmm)
A trigonometric equation is an equation that involves one or more trigonometric functions, such as sine, cosine, or tangent, and an unknown variable. The goal of solving a trigonometric equation is to find the value(s) of the variable that make the equation true.
The basic trigonometric identities include the Pythagorean identities, which relate the three main trigonometric functions (sine, cosine, and tangent) to each other and to the unit circle. Other important identities include the reciprocal identities, quotient identities, and even-odd identities.
To solve a trigonometric equation, you can use algebraic methods, such as factoring, combining like terms, and isolating the variable. You can also use trigonometric identities to simplify the equation and make it easier to solve. In some cases, you may need to use a calculator or graphing software to find the solutions.
The domain of a trigonometric equation refers to the set of all possible values for the independent variable (usually denoted as x) that make the equation defined. In general, the domain of a trigonometric equation is all real numbers, but there may be restrictions depending on the specific trigonometric function and equation.
Trigonometric equations have many real-world applications, including in engineering, physics, architecture, and navigation. For example, trigonometric equations can be used to calculate the height of a building, the distance between two objects, or the angles of a triangle. They are also essential in solving problems involving waves, vibrations, and periodic phenomena.