Kristi-Anne Gonzalez’s

Trigonometry for Dummies

Trigonometry is "the study of angles and angular relationships of planar and three-dimensional figures“.

To learn trigonometry, you must first understand the basics of a right triangle.

The sides titled "a" and "b" are also known as the legs of the triangle, while "c" is the hypotenuse (the longest side of the right triangle).

The angle displayed with a small square is the right angle, or 90 degrees. It is always opposite the hypotenuse.

With the formula a^2 + b^2 = c^2, you can use the measurements of the legs to find that of the hypotenuse.

If some of the sides or angles of the right triangle are missing, you always resort to SOH CAH TOA.

Plug in the values of the sides you already have to find the missing values.

To find the exact measurement of an angle, plug it into a graphic calculator.

unit circle - a circle whose has a radius equal to one

(x,y) or (cos, sin)

coterminal angles - angles sharing the same initial (beginning) and terminal (ending) sides

To find the coterminal angle of a given angle, you must use the equation:

• angle - x = 360 degrees (if angle is positive)

• 360 degrees - angle = x (if angle is negative)

If given an angle of 400 degrees and asked to find its coterminal angle, you must use the equation and you will get an answer of 40 degrees.

You may also want to draw it out on a unit circle to better your understanding (right).

positive rotation - counter clock-wise; used for positive anglesnegative rotation - clock-wise; used for negative angles

reference angle - an acute angle (less than 90 degrees) formed by the terminal side of an angle and the x-axis

An example would be of a 225 degree angle.

to find the reference angle, you subtract the angle from the nearest x-axis.225 - 180 = 45

Hence, the reference angle of 225 degrees would be 45 degrees.

Again, you can depict this on a unit circle to fully comprehend the concept.

Each quadrant of a coordinate plain represents a different trigonometric function.The order in which the quadrants are titled is counter clock-wise.In the picture below, to the right, you notice the letters A, S, T, and C.

A = allS = sineT = tangentC = cosine

A simpler way to memorize this is by using the acronym, but changing its meaning to "All Students Take Classes". I hope that helps.

There are 2pi radians in a complete circle, and pi radians in a half circle (displayed below to the left)

The ordered pairs outside the circle is in degrees,

while the fractions inside the circle is in radians

This is a table display of the circle shown in the previous slide

To the right is a list of the reciprocals of Sine, Cosine, and Tangent. From them, Cosecant, Secant, and Cotangent are derived

You are no longer a dummy