Symmetry and Periodicity of Trigonometric Functions
Precalculus · Flashcards
PRECALCULUS · FLASHCARDS
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QUESTION
What symmetry identity relates
sin
(
−
θ
)
\sin(-\theta)
sin
(
−
θ
)
to
sin
θ
\sin\theta
sin
θ
?
QUESTION
What symmetry identity relates
tan
(
−
θ
)
\tan(-\theta)
tan
(
−
θ
)
to
tan
θ
\tan\theta
tan
θ
?
QUESTION
What periodicity identity shows
tan
(
θ
+
π
)
\tan(\theta+\pi)
tan
(
θ
+
π
)
in simplest form?
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ANSWER
tan
(
θ
+
π
)
=
tan
θ
\tan(\theta+\pi)=\tan\theta
tan
(
θ
+
π
)
=
tan
θ
. Tangent has period
π
\pi
π
, so adding
π
\pi
π
returns the same value.
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