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A point P(x, y) is shown of the unit circle corresponding to a real number θ. Find the values of the six trigonometric functions of θ.

A Point Px Y Is Shown Of The Unit Circle Corresponding To A Real Number Θ Find The Values Of The Six Trigonometric Functions Of Θ class=

Sagot :

The sine of theta is given by the y-coordinate of point P:

[tex]\sin (\theta)=\frac{15}{17}[/tex]

The cosine of theta is given by the x-coordinate of point P, so we have:

[tex]\cos (\theta)=-\frac{8}{17}[/tex]

The tangent can be calculated as the sine divided by the cosine:

[tex]\tan (\theta)=\frac{\sin(\theta)}{\cos(\theta)}=\frac{\frac{15}{17}}{-\frac{8}{17}}=-\frac{15}{8}[/tex]

The cosecant is the inverse of the sine:

[tex]\csc (\theta)=\frac{1}{\sin (\theta)}=\frac{17}{15}[/tex]

The secant is the inverse of the cosine:

[tex]\sec (\theta)=\frac{1}{\text{cos(}\theta)}=-\frac{17}{8}[/tex]

And the cotangent is the inverse of the tangent:

[tex]\cot (\theta)=\frac{1}{\tan(\theta)}=-\frac{8}{15}[/tex]

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