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For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse.
The Trigonometric Identities are equations that are true for Right Angled Triangles. (If it isn't a Right Angled Triangle use the Triangle Identities page) Each side of a right triangle has a name: Adjacent is always next to the angle. And Opposite is opposite the angle.
The main trigonometric identities are Pythagorean identities, reciprocal identities, sum and difference identities, and double angle and half-angle identities. For the non-right-angled triangles, we will have to use the sine rule and the cosine rule.
What is an identity? How do we verify an identity? Consider the trigonometric equation \ (\sin (2x) = \cos (x)\). Based on our current knowledge, an equation like this can be difficult to solve exactly because the periods of the functions involved are different.
Trigonometric identities are equations that are used to describe the many relationships that exist between the trigonometric functions. Among other uses, they can be helpful for simplifying trigonometric expressions and equations.
Key Questions. How do you use the fundamental trigonometric identities to determine the simplified form of the expression? "The fundamental trigonometric identities" are the basic identities: •The reciprocal identities •The pythagorean identities •The quotient identities. They are all shown in the following image:
Lists the basic trigonometric identities, and specifies the set of trig identities to keep track of, as being the most useful ones for calculus.
