Neil Simonetti

**1. Select a Trigonometric Calculation.**

Choose a trigonometric function and angle

You need to select a function and angle before continuing.

**2. Translate angle to degrees.**

If you are not familiar with angles in radians, convert to degrees.

Angle in degrees = °

Since a full circle has 360° which is also 2π radians,
multiplying the radians value by the ratio ^{360}/_{2π}
(or ^{180}/_{π} in reduced from) will
give you the value of the angle in degrees.

**3. Sketch the angle on the unit circle.**

Click on the point on the unit circle corresponding to the angle.

Positive angles are drawn counter-clockwise from the positive *x*-axis.

Negative angles are drawn clockwise from the positive *x*-axis.

**4. Determine the coordinates.**

*x* coordinate =

*y* coordinate =

Note: for √2, type “r2”,
for √3, type “r3”,
for √4, just type “2”.

Thus, to enter √¾, type “r3/2”.

If the point is a simple compass point (north, south, east, or west), one of the coordinates
will be zero, and the other will be 1 or −1.

Otherwise, you may need to choose one of the two triangles below to place inside the
unit circle to help determine the coordinates (click on a triangle to see).
**Not that triangle.**
**This problem does not need a triangle.**

**5. Identify the trigonometric function in terms of x and y.**

Each trigonometric function is a ratio involving

Trigonometic ratio for =

Each trigonometric function is defined as a ratio of side lengths in a right triangle.

cos θ = | adj | = | x |
sin θ = | opp | = | y |
|||

hyp | 1 | hyp | 1 | |||||||

tan θ = | opp | = | y |
cot θ = | adj | = | x |
|||

adj | x | opp | y | |||||||

sec θ = | hyp | = | 1 | csc θ = | hyp | = | 1 | |||

adj | x | opp | y | |||||||

**6. Final calculation.**

Use the trigonometric ratio with the coordinates to calculate (and simplify) the final answer.

Final calculation for
**() =**

For √2, type “r2”.
Type “undefined” if you need to divide by zero.

( | a |
) | × c |
When confronted by a compound fraction, you can simplify it by multiplying the top and bottom of the large fraction by the common denominator of the small fractions. |

c | ||||

( | b |
) | × c | |

c |

**7. Select a new problem at step 1.**