Answered

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Hi! I was absent in class and did not understand this lesson please I will be really grateful if you help me ! I appreciate it this is classwork assignment does not count as a test

Hi I Was Absent In Class And Did Not Understand This Lesson Please I Will Be Really Grateful If You Help Me I Appreciate It This Is Classwork Assignment Does No class=

Sagot :

ANSWER

[tex]\frac{240}{289}[/tex]

EXPLANATION

We want to find the value of the expression using the given figure:

[tex]\sin (2\theta)[/tex]

To do this, let us rewrite the expression in terms of its trigonometric identity:

[tex]\sin (2\theta)=2\sin \theta\cos \theta[/tex]

To solve this we can apply trigonometric ratios SOHCAHTOA for right triangles to find the values of sine and cosine:

[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \end{gathered}[/tex]

For the given triangle, we have that:

[tex]\begin{gathered} \sin \theta=\frac{8}{17} \\ \cos \theta=\frac{15}{17} \end{gathered}[/tex]

Therefore, the value of the expression is:

[tex]\begin{gathered} \sin 2\theta=2\cdot\frac{8}{17}\cdot\frac{15}{17} \\ \sin 2\theta=\frac{240}{289} \end{gathered}[/tex]

That is the answer.

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