Therefore, the distance from p to 2p can also be notated as 0 to -p, depending on which way you travel the circle. Relationships between angles are important:. For the purpose of the trig cheat sheet, and conventionally, if the sides of a triangle are labeled a, b, c then the angles are ABC, where A is the angle made by b and c, B is the angle made by a and c, and C is the angle made by a and b.
A is called the opposite angle of a, and a is the opposite side of A. Much of trigonometry is based on triangles, usually right or acute. Your notes or textbook may use x and y or other variables, but the meanings are the same. Right Triangle and Sine, Cosine, Tangent. The chart below gives a breakdown of the trig functions and their relationship to right triangles and the unit circle.
Here is a simple way to remember the right triangle relationships: Hold up your left hand, palm facing out, fingers together and thumb sticking out the right like an L.
Now, imagine a line from the tip of your forefinger to the tip of your thumb. If you pretend the curve where your thumb meets your hand is a right angle, then you have a right triangle. Your thumb is a, your forefinger is b, and the imaginary line the hypotenuse is c. Then the angle at the tip of your forefinger is A, the tip of your thumb is B and the right angle is C. Now, use that to memorize the following definitions:. The trig cheat sheet only gives the formulas for these theorems.
If you are required to use the full definition, or are unsure when to use each formula, you will need additional study material. Pythagorean Theorem, Law of Sines, Law of Cosines, Law of Tangents are all about the relationships between the sides and angles of triangles. Using the definition of a right triangle on your hand as explained above the lengths of the sides are related by the following formula:.
When the angle C is p, 0, or 2p, the law of cosines reduces to a simpler formula. If it is easier for you to memorize these too, go ahead, but usually I just solve for them. Now take the square root of both sides.
Remember that r represents the radius of a circle. So even though there are two values for r that you could square to get So let's only consider the positive value of r:. You showed me what I messed up on. Thank you so much. I was squaring 66 in the equation because it's meters squared. Appreciate the help friend.
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