Trig Functions

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Use Trigonometry to Measure the View of Satellite Cameras


Sine and Cosine with Algebra


Domains and Ranges of Trigonometry Functions


The Sine Function: Opposite over Hypotenuse


The Cosine Function: Adjacent over Hypotenuse


How to Locate Reference Angles


Assign Negative and Positive Trig Functions by Quadrant


Use 6 Different Ratios of a Right Triangle

Each of the three sides of a right triangle — hypotenuse, opposite, and adjacent — has a respective length or measure. And those three lengths or measures form six different ratios. Check out the following [more…]

The Cosecant and Secant Functions

The cosecant function, abbreviated csc, is the reciprocal of the sine function and thus uses this ratio: hypotenuse/opposite. The hypotenuse of a right triangle is always the longest side, so the numerator [more…]

The Cotangent Function

The last reciprocal function is the cotangent,abbreviated cot. This function is the reciprocal of the tangent (hence, the co-). The ratio of the sides for the cotangent is adjacent/opposite. [more…]

Positive and Negative Angles on a Unit Circle

The unit circle is a platform for describing all the possible angle measures from 0 to 360 degrees, all the negatives of those angles, plus all the multiples of the positive and negative angles from negative [more…]

Use Coordinates of Points to Find Values of Trigonometry Functions

One way to find the values of the trig functions for angles is to use the coordinates of points on a circle that has its center at the origin. Letting the positive [more…]

The Tangent Function: Opposite over Adjacent

The third trig function, tangent, is abbreviated tan. This function uses just the measures of the two legs and doesn’t use the hypotenuse at all. The tangent is described with this ratio: opposite/adjacent [more…]

How to Create a Table of Trigonometry Functions

The angles used most often in trig have trig functions with convenient exact values. Other angles don’t cooperate anywhere near as nicely as these popular ones do. A quick, easy way to memorize the exact [more…]

How to Find a Missing Coordinate on a Unit Circle

If you have the value of one of a point’s coordinates on the unit circle and need to find the other, you can substitute the known value into the unit-circle equation and solve for the missing value. [more…]

Find the Trigonometry Function of an Angle in a Unit Circle

You can determine the trig functions for any angles found on the unit circle — any that are graphed in standard position (meaning the vertex of the angle is at the origin, and the initial side lies along [more…]

Domain and Range of Tangent and Cotangent Trigonometry Functions

The tangent and cotangent are related not only by the fact that they’re reciprocals, but also by the behavior of their ranges. In reference to the coordinate plane, tangent is [more…]

Domain and Range of Cosecant and Secant Trigonometry Functions

The cosecant and secant functions are closely tied to sine and cosine, because they're the respective reciprocals. In reference to the coordinate plane, cosecant is [more…]


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