Trig Equations
Solving equations involving trigonometric functions and understanding solution domains
Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)
Solving sinθ=a
Since sinθ represents the y-coordinate of a point on the unit circle, solving the equation
is equivalent to drawing the line y=a, finding the intersections with the unit circle, and determining the angle of these intersections relative to the positive x-axis.
This helps visualize all the possible solutions. For
the solutions are
Solving cosθ=a
Since cosθ represents the x-coordinate of a point on the unit circle, solving the equation
is equivalent to drawing the line x=a, finding the intersections with the unit circle, and determining the angle of these intersections relative to the positive x-axis.
This helps visualize all the possible solutions. For
the solutions are
Solving tan(x)=a
Since tanθ represents the angle between the line y=xtanθ and the x-axis, solving
is equivalent to drawing the line y=a, and measuring the minor and major angles it forms with the x-axis:
Solving trig equations algebraically in specific domain
When we have a trig equation where the argument to the trig function is of the form ax+b, we need to find the domain of ax+b using the domain of x. For example, if 0≤x<2π and we have sin(2x+2π)=1, then
therefore
Trigonometric Quadratics
Trigonometric functions can also show up in pseudo-quadratics - a quadratic where the variable being squared is not x but a trig function.
On exams, these equations often require using the Pythagorean identity sin2θ+cos2θ=1.
Nice work completing Trig Equations, here's a quick recap of what we covered:
Skills covered
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