Question

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.

Answer 1

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

`\sin (\theta)=(15)/(17)`

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

`\cos (\theta)=-(8)/(17)`

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

`\tan (\theta)=(\sin(\theta))/(\cos(\theta))=((15)/(17))/(-(8)/(17))=-(15)/(8)`

The cosecant is the inverse of the sine:

`\csc (\theta)=(1)/(\sin (\theta))=(17)/(15)`

The secant is the inverse of the cosine:

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

And the cotangent is the inverse of the tangent:

`\cot (\theta)=(1)/(\tan(\theta))=-(8)/(15)`