Trigonometric Mind Map (Edward Lowery)
Six Trig Functions and Identities
Sine (sin)
sin=y
Cosine (cos)
cos=x
Tangent (tan)
tan=y/x
All of these (from left to right of this split) are reciprocals of each other in respective order. They also relate to the unit circle (below).
Cosecant (csc)
csc=1/y
Secant (sec)
sec=1/x
Cotangent (cot)
cot=x/y
Inverses and their properties
These are used when asked to find exact values of certain equations that include inverses. Remember to make sure they fit in the range in order to make the answer is correct.
Trig Identities
Use these identities when asked to either prove an identity or solve an equation. Remember that one can switch any of these identites around as long as it algebraically works out.
Law of Sine
Law of sine is the easier of the two when asked to solve a triangle. Use this when you have at least 2 sides and a corresponding angle or the other way around.
Law of Cosine
Law of Cosine can be used when asked to solve a triangle and the law of sine doesn't work. It is a bit more complicated but it works. (Don't use law of sine when you start solving with the law of cosine, it could give you the wrong solution!!).
Area Formulas for triangles
Use the formula on the top that is equal to A when you have a SAS triangle (Side-Angle-Side). Use the formula that includes S and the formula that is close to the distance formula for a SSS triangle.A better expleantion is made by the video below.