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WOLFRAM|DEMONSTRATIONS PROJECT

Geometric Solution of a Trigonometric Equation

​
δ
0.5
μ
0.6
sin γ = sin μ cos δ
This Demonstration shows a geometric solution for the trigonometric equation
sinγ=sinμcosδ
for the unknown
γ
. Let
ABC
be a right triangle with one leg
AB=sinμ
and hypotenuse
AC
of length 1. Draw a circle with center the midpoint of
AC
and radius 1/2. Draw a ray through
A
at an angle
δ
with respect to
AB
. The orthogonal projection
AE
of
AB
onto the ray has length
sinμcosδ
. Let
G
be a point of the circle such that
AE=AG
. Then the solution is
γ=∠ACG
.
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