Proving Angle Addition/Subtraction Formulas
Precalculus · Flashcards · Recall
PRECALCULUS · FLASHCARDS
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QUESTION
State the formula for
cos
(
α
+
β
)
\cos(\alpha+\beta)
cos
(
α
+
β
)
in terms of
sin
\sin
sin
and
cos
\cos
cos
.
QUESTION
What denominator condition must hold for
tan
(
α
−
β
)
\tan(\alpha-\beta)
tan
(
α
−
β
)
to be defined from its formula?
QUESTION
State the rotation matrix
R
(
θ
)
R(\theta)
R
(
θ
)
used in a common proof of angle addition formulas.
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ANSWER
R
(
θ
)
=
(
cos
θ
−
sin
θ
s
i
n
θ
cos
θ
)
R(\theta)=\begin{pmatrix}\cos\theta&-\sin\theta\\sin\theta&\cos\theta\end{pmatrix}
R
(
θ
)
=
(
cos
θ
s
in
θ
−
sin
θ
cos
θ
)
. Standard 2D rotation matrix for counterclockwise rotation.
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