Trigonometry Basics

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How to Change the Amplitude, Period, and Position of a Tangent or Cotangent Graph

You can transform the graph for tangent and cotangent vertically, change the period, shift the graph horizontally, or shift it vertically. However, you should take each transformation one step at a time [more…]

How to Simplify an Expression Using Reciprocal Identities

When you're asked to simplify an expression involving cosecant, secant, or cotangent, you change the expression to functions that involve sine, cosine, or tangent, respectively. When you change functions [more…]

How to Graph a Secant Function

You can graph a secant function f(x) = sec x by using steps similar to those for tangent and cotangent. As with tangent and cotangent, the graph of secant has asymptotes. This is because secant is defined [more…]

How to Plot the Major Angles of the Whole Unit Circle

You can take the unit-circle angles and the special right triangles and put them together to create a neat little package: the full unit circle. You create special triangles on the unit circle one at a [more…]

How to Change the Amplitude, Period, and Position of a Secant or Cosecant Graph

If you have to change the amplitude, period, and position of a secant or cosecant graph, your best bet is to graph their reciprocal functions and transform them first. The reciprocal functions, sine and [more…]

How to Graph a Sine Function

Knowing how to graph trig functions allows you to measure the movement of objects that move back and forth or up and down in a regular interval, such as pendulums. Sine functions are perfect ways of expressing [more…]

How to Graph a Tangent Function

The tangent function has a parent graph just like any other function. Using the graph of this function, you can make the same type of transformation that applies to the parent graph of any function. The [more…]

How to Prove a Trigonometric Identity Containing a Square Root

When a square root appears inside a trigonometric identity, and you know both sides are equal, you have to square both sides at some point to finish the proof. However, if you don't know both sides are [more…]

How to Calculate the Tangent of an Angle

Because a lot of pre-calculus work involves trigonometric functions, you need to understand ratios. One important ratio in right triangles is the tangent. The tangent of an angle theta, or [more…]

Working with Trigonometric Ratios on the Coordinate Plane

To put angles on the coordinate plane, essentially all you do is look at the trig ratios in terms of x and y values rather than opposite, adjacent, and hypotenuse. Redefining these ratios to fit the coordinate [more…]

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