Proving the Pythagorean Identity
Precalculus · Flashcards
PRECALCULUS · FLASHCARDS
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QUESTION
What is
sin
(
θ
)
\sin(\theta)
sin
(
θ
)
if
cos
(
θ
)
=
5
13
\cos(\theta)=\frac{5}{13}
cos
(
θ
)
=
13
5
and
θ
\theta
θ
is in Quadrant I?
QUESTION
Find
cos
(
θ
)
\cos(\theta)
cos
(
θ
)
if
sin
(
θ
)
=
3
5
\sin(\theta)=\frac{3}{5}
sin
(
θ
)
=
5
3
and
θ
\theta
θ
is in Quadrant I.
QUESTION
What identity relates
sin
2
(
θ
)
\sin^2(\theta)
sin
2
(
θ
)
and
cos
2
(
θ
)
\cos^2(\theta)
cos
2
(
θ
)
for any angle
θ
\theta
θ
?
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ANSWER
sin
2
(
θ
)
+
cos
2
(
θ
)
=
1
\sin^2(\theta)+\cos^2(\theta)=1
sin
2
(
θ
)
+
cos
2
(
θ
)
=
1
. Fundamental trig identity that holds for all angles.
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