Question
Consider a right triangle where the measure of one of the acute angles is
a
°
.
If
s
i
n
(
a
°
)
=
x
,
then the cosine of which angle must also be equal to
x
?
Consider a right triangle where the measure of one of the acute angles is
a
°
.
If
s
i
nConsider a right triangle where the measure of one of the acute angles is
a
°
.
If
s
i
n
(
a
Consider a right triangle where the measure of one of the acute angles is
a
°
.
If
s
i
n
(
a
°
)
=
x
,
then the cosine of which angle must also be equal to
x
?
a
°
.
If
s
i
n
(
a
°
)
=
x
,
then the cosine of which angle must also be equal to
x
?
Consider a right triangle where the measure of one of the acute angles is
a
°
.
If
s
i
nConsider a right triangle where the measure of one of the acute angles is
a
°
.
If
s
i
n
(
a
Consider a right triangle where the measure of one of the acute angles is
a
°
.
If
s
i
n
(
a
°
)
=
x
,
then the cosine of which angle must also be equal to
x
?
Answers
GPT-4o mini
In a right triangle, the angles are such that one is \(90^\circ\) and the other two are acute angles whose measures add up to \(90^\circ\). If you have an acute angle \(a^\circ\) and you know that \(\sin(a^\circ) = x\), you can find the cosine of the complementary angle, which is \(90^\circ - a^\circ\).
According to the co-function identities in trigonometry, the sine of an angle is equal to the cosine of its complementary angle:
\[
\sin(a^\circ) = \cos(90^\circ - a^\circ)
\]
Given that \(\sin(a^\circ) = x\), it follows that:
\[
\cos(90^\circ - a^\circ) = x
\]
Thus, if \(\sin(a^\circ) = x\), then:
\[
\cos(90^\circ - a^\circ) = x
\]
So the cosine of the angle \(90^\circ - a^\circ\) must also be equal to \(x\).
According to the co-function identities in trigonometry, the sine of an angle is equal to the cosine of its complementary angle:
\[
\sin(a^\circ) = \cos(90^\circ - a^\circ)
\]
Given that \(\sin(a^\circ) = x\), it follows that:
\[
\cos(90^\circ - a^\circ) = x
\]
Thus, if \(\sin(a^\circ) = x\), then:
\[
\cos(90^\circ - a^\circ) = x
\]
So the cosine of the angle \(90^\circ - a^\circ\) must also be equal to \(x\).