Find the exact values of the three trignometric functions of the angle

\theta

( \sin \theta , \cos \theta , \tan \theta )

of the two triangles shown below. Is the function values are the same? Explain. $Find the exact values of the three trignometric functions of the angle \theta ( \sin \theta , \cos \theta , \tan \theta ) of the two triangles shown below. Is the function values are the same? Explain. A) \sin \theta _ { 1 } = \frac { 5 } { 13 } , \cos \theta _ { 1 } = \frac { 12 } { 13 } , \tan \theta _ { 1 } = \frac { 5 } { 12 } \sin \theta = \frac { 6.5 } { 2.5 } = \frac { 13 } { 5 } , \cos \theta = \frac { 6.5 } { 6 } = \frac { 13 } { 12 } , \tan \theta = \frac { 6 } { 2.5 } = \frac { 12 } { 5 } The function values are different because the traingles are not similar and corresponding sides are not proportional. B) \sin \theta = \frac { 12 } { 13 } , \cos \theta = \frac { 5 } { 13 } , \tan \theta = \frac { 5 } { 12 } \sin \theta = \frac { 6 } { 6.5 } = \frac { 12 } { 13 } , \cos \theta = \frac { 2.5 } { 6.5 } = \frac { 5 } { 13 } , \tan \theta = \frac { 2.5 } { 6.5 } = \frac { 5 } { 12 } The function values are the same because the traingles are similar and corresponding sides are proportional. C) \sin \theta = \frac { 5 } { 13 } , \cos \theta = \frac { 12 } { 13 } , \tan \theta = \frac { 5 } { 12 } \sin \theta = \frac { 2.5 } { 6.5 } = \frac { 5 } { 13 } , \cos \theta = \frac { 6 } { 6.5 } = \frac { 12 } { 13 } , \tan \theta = \frac { 2.5 } { 6 } = \frac { 5 } { 12 } The function values are the same because the traingles are similar and corresponding sides are proportional. D) \sin \theta = \frac { 13 } { 5 } , \cos \theta = \frac { 13 } { 12 } , \tan \theta _ { 1 } = \frac { 5 } { 12 } \sin \theta = \frac { 6.5 } { 2.5 } = \frac { 13 } { 5 } , \cos \theta = \frac { 6.5 } { 6 } = \frac { 13 } { 12 } , \tan \theta = \frac { 2.5 } { 6 } = \frac { 5 } { 12 } The function values are the same because the traingles are similar and corresponding sides are proportional. E) \sin \theta = \frac { 13 } { 5 } , \cos \theta = \frac { 13 } { 12 } , \tan \theta = \frac { 5 } { 12 } \sin \theta = \frac { 6.5 } { 5 } = \frac { 13 } { 2.5 } , \cos \theta = \frac { 6.5 } { 12 } = \frac { 13 } { 6 } , \tan \theta = \frac { 2.5 } { 12 } = \frac { 5 } { 6 } The function values are different because the traingles are not similar and corresponding sides are not proportional.$
A)

\sin \theta _ { 1 } = \frac { 5 } { 13 } , \cos \theta _ { 1 } = \frac { 12 } { 13 } , \tan \theta _ { 1 } = \frac { 5 } { 12 }

\sin \theta = \frac { 6.5 } { 2.5 } = \frac { 13 } { 5 } , \cos \theta = \frac { 6.5 } { 6 } = \frac { 13 } { 12 } , \tan \theta = \frac { 6 } { 2.5 } = \frac { 12 } { 5 }

The function values are different because the traingles are not similar and corresponding sides are not proportional.
B)

\sin \theta = \frac { 12 } { 13 } , \cos \theta = \frac { 5 } { 13 } , \tan \theta = \frac { 5 } { 12 }

\sin \theta = \frac { 6 } { 6.5 } = \frac { 12 } { 13 } , \cos \theta = \frac { 2.5 } { 6.5 } = \frac { 5 } { 13 } , \tan \theta = \frac { 2.5 } { 6.5 } = \frac { 5 } { 12 }

The function values are the same because the traingles are similar and corresponding sides are proportional.
C)

\sin \theta = \frac { 5 } { 13 } , \cos \theta = \frac { 12 } { 13 } , \tan \theta = \frac { 5 } { 12 }

\sin \theta = \frac { 2.5 } { 6.5 } = \frac { 5 } { 13 } , \cos \theta = \frac { 6 } { 6.5 } = \frac { 12 } { 13 } , \tan \theta = \frac { 2.5 } { 6 } = \frac { 5 } { 12 }

The function values are the same because the traingles are similar and corresponding sides are proportional.
D)

\sin \theta = \frac { 13 } { 5 } , \cos \theta = \frac { 13 } { 12 } , \tan \theta _ { 1 } = \frac { 5 } { 12 }

\sin \theta = \frac { 6.5 } { 2.5 } = \frac { 13 } { 5 } , \cos \theta = \frac { 6.5 } { 6 } = \frac { 13 } { 12 } , \tan \theta = \frac { 2.5 } { 6 } = \frac { 5 } { 12 }

The function values are the same because the traingles are similar and corresponding sides are proportional.
E)

\sin \theta = \frac { 13 } { 5 } , \cos \theta = \frac { 13 } { 12 } , \tan \theta = \frac { 5 } { 12 }

\sin \theta = \frac { 6.5 } { 5 } = \frac { 13 } { 2.5 } , \cos \theta = \frac { 6.5 } { 12 } = \frac { 13 } { 6 } , \tan \theta = \frac { 2.5 } { 12 } = \frac { 5 } { 6 }

The function values are different because the traingles are not similar and corresponding sides are not proportional.

Use the Value of the Trigonometric Function to Find The \sin

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