Trigonometry For Dummies
Book image
Explore Book Buy On Amazon

Calculating trig functions of angles within a unit circle is easy as pie. The figure shows a unit circle, which has the equation x2 + y2 = 1, along with some points on the circle and their coordinates.

image0.jpg

Using the angles shown, find the tangent of theta.

  1. Find the x- and y-coordinates of the point where the angle’s terminal side intersects with the circle.

    The coordinates are

    image1.jpg
    image2.jpg

    The radius is r = 1.

  2. Determine the ratio for the function and substitute in the values.

    The ratio for the tangent is y/x, so you find that

    image3.jpg

Next, using the angles shown, find the cosine of sigma.

  1. Find the x- and y-coordinates of the point where the terminal side of the angle intersects with the circle.

    The coordinates are

    image4.jpg
    image5.jpg

    the radius is r = 1.

  2. Determine the ratio for the function and substitute in the values.

    The ratio for the cosine is x/r, which means that you need only the x-coordinate, so

    image6.jpg

Now, using the angles shown, find the cosecant of beta.

  1. Find the x- and y-coordinates of the point where the terminal side of the angle intersects with the circle.

    The coordinates are x = 0 and y = –1; the radius is r = 1.

  2. Determine the ratio for the function and substitute in the values.

    The ratio for cosecant is r/y, which means that you need only the y-coordinate, so

    image7.jpg

About This Article

This article is from the book:

About the book author:

Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others.

This article can be found in the category: