189k views
0 votes
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 P(x, y) is shown of the unit circle corresponding to a real number θ. Find-example-1

1 Answer

4 votes

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)

User Andrucz
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories