How to Calculate Trigonometry Functions of Angles Using the Unit Circle - dummies

# How to Calculate Trigonometry Functions of Angles Using the Unit Circle

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.

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

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

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

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

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