Some basic trigonometric functions are sin, cos, and tan. As well their inverse functions are csc, sec, and cot.
To understand how to find these trig functions on a triangle SOH CAH TOA is an easy phrase to remember.
Meaning:
A trigonometric identity, are equations that are true for all variables of right angled triangles. It is the proving of an identity or function, so that both sides of the equation are true for each other.
Reciprocal Identities are trigonometric identities of sec, csc, and cot, that are represented in terms of sin, cos, and tan.
A quotient identity deals with tan and cot functions and their relationships with cos and sin.
Even or Odd Trig Identities
As shown above only cos and sec functions are even, leaving csc, sin, tan, and cot all as odd functions.
Next are the three main Pythagorean Identities:
They can all be transformed into other identities through the simple use of the addition and subtraction property.
The first identity that is stared in yellow is the main identity. Both of the bottom two identities have been derived from the first identity. This is shown below:
When applying these skills to solving identities, there is no one specific way to solve the problem. As either side of the equation can be worked, and the pythagorean identities can be used differently.
Examples:
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