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For a standard position angle determined by the point (x,y) what are the values of the trigonometric functions?
For te point (5,12), find csc theta and sec theta

Respuesta :

metchelle
For the standard position triangle having sides of x=5 and y=12 and the included theta, the hypotenuse can be estimated through the pythagorean theorem and is equal to 13, with this sin theta equals 12/13 and cosine theta = 5/13, since csc theta = 1/sin theta and sec theta = 1/cos theta, therefore, csc theta = 13/12 and sec theta = 13/5
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Answer:

[tex]cosec{\theta}=\frac{13}{12}[/tex] and [tex]sec{\theta}={\frac{13}{5}}[/tex]

Step-by-step explanation:

For the standard position triangle having sides of x=5 and y=12 and the included theta, the hypotenuse can be calculated through the Pythagorean theorem such as:

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

[tex](AC)^2=144+25[/tex]

[tex](AC)^2=169[/tex]

[tex](AC)=13[/tex]

Therefore, the value of AC(Hypotenuse) is 13 units.

Now, [tex]cosec{\theta}={\frac{AC}{AB}}[/tex]

⇒[tex]cosec{\theta}=\frac{13}{12}[/tex]

Also, [tex]sec{\theta}=\frac{AC}{BC}[/tex]

⇒[tex]sec{\theta}={\frac{13}{5}}[/tex]

which are the required values of [tex]cosec{\theta}[/tex] and [tex]sec{\theta}[/tex].

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