Proving the Pythagorean Identity
Geometry · Flashcards
GEOMETRY · FLASHCARDS
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QUESTION
Identify the right-triangle relation used to prove
sin
2
(
θ
)
+
cos
2
(
θ
)
=
1
\sin^2(\theta)+\cos^2(\theta)=1
sin
2
(
θ
)
+
cos
2
(
θ
)
=
1
.
QUESTION
Identify the correct value: if
cos
(
θ
)
=
−
3
2
\cos(\theta)=-\frac{\sqrt{3}}{2}
cos
(
θ
)
=
−
2
3
in Quadrant III, what is
sin
(
θ
)
\sin(\theta)
sin
(
θ
)
?
QUESTION
Find
sin
(
θ
)
\sin(\theta)
sin
(
θ
)
if
tan
(
θ
)
=
3
4
\tan(\theta)=\frac{3}{4}
tan
(
θ
)
=
4
3
and
θ
\theta
θ
is in Quadrant I.
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ANSWER
sin
(
θ
)
=
3
5
\sin(\theta)=\frac{3}{5}
sin
(
θ
)
=
5
3
. From
tan
(
θ
)
=
3
4
\tan(\theta)=\frac{3}{4}
tan
(
θ
)
=
4
3
, use identity
1
+
tan
2
(
θ
)
=
sec
2
(
θ
)
1+\tan^2(\theta)=\sec^2(\theta)
1
+
tan
2
(
θ
)
=
sec
2
(
θ
)
to find sine.
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