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\\[\\var{a}\\sin(x)=\\var{a-1}\\]

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$\\sin(x)=$ [[0]]

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$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$

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\\[\\var{b}\\cos(x)=\\var{c}\\]

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$\\cos(x)=$ [[0]]

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$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$

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\\[\\var{b+1}\\cos(x)=-\\var{b-1}\\]

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$\\cos(x)=$ [[0]]

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$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$

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\\[\\var{c+3}\\sin(x)=-\\var{c}\\]

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$\\sin(x)=$ [[0]]

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$x=$ [[1]]$^\\circ$, [[2]]$^\\circ$, [[3]]$^\\circ$ or [[4]]$^\\circ$

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Discard any solutions out of range.

"}], "name": "Trigonometric Equations 1 - Simple (Degrees)", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "

Simple trig equations with degrees

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Solve the following equations in degrees, for $x$ in the range $0^\\circ\\leq x\\leq720^\\circ$.

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Give your answers correct to the nearest degree in ascending order.

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Firstly, isolate the trigonometric function on one side of the equation.

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Then perform the appropriate inverse trigonometric function on both sides to find the argument.

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Finally, if the argument is an equation or function of the variable you want to find, manipulate your results accordingly.

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For example, if the solutions for the argument of $\\sin(2x)=a$, where $a$ is a number or function, were found to be $46^\\circ$ and $134^\\circ$ within the given range, further operations would be necessary to find the solutions for $x$.

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Here, the first results would be halved and $x$ would therefore be equal to $23^\\circ$ and $67^\\circ$.

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