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.
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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.
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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.
Trigonometry - Mathematics A-Level Revision
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. Here is a list of the most important trig formulas. Squared formulas. Sum and Difference formulas a and b are angles. Power Reduction Formulas. Product to Sum Formulas a and b are angles.
Sum to Product Formulas a and b are angles. Bright Hub Education. The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner:. The main functions in trigonometry are Sine, Cosine and Tangent. Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.
The triangle could be larger, smaller or turned around, but that angle will always have that ratio.
We can't reach the top of the tree, so we walk away and measure an angle using a protractor and distance using a laser :. What does the 0. It is the ratio of the side lengths, so the Opposite is about 0. Note: you can see the nice graphs made by sine, cosine and tangent.
Trigonometry For Dummies Cheat Sheet
Angles can be in Degrees or Radians. Here are some examples:. Because the angle is rotating around and around the circle the Sine, Cosine and Tangent functions repeat once every full rotation see Amplitude, Period, Phase Shift and Frequency. It helps us in Solving Triangles.
When we know any 3 of the sides or angles we can find the other 3 except for the three angles case. See Solving Triangles for more details. Similar to Sine, Cosine and Tangent, there are three other trigonometric functions which are made by dividing one side by another:. The Trigonometric Identities are equations that are true for all right-angled triangles.