Abstract
This chapter discusses identities and inverse functions. Because the six trigonometric functions are so closely related to each other, there is a multitude of identities interconnecting them. The first identity, sin2θ + cos2θ =1, is an immediate consequence of the very definition of sin θ and cos θ, whereby cos θ, sin θ is a point on the unit circle. To derive the second identity, tan2θ + 1 = sec2θ, both sides of the first identity must be divided by cos2θ. To derive the third, 1 + cot2 θ = cosec2θ, both sides of the first identity must be divided by sin2θ. Each trigonometric function can be expressed in terms of any one of the other five. In polar coordinates, the grid lines are all circles centered at (0, 0), and all rays are from (0, 0). Each point (x, y) different from (0, 0) is the intersection of one circle and one ray. The circle is identified by a positive number r, its radius, and the ray is identified by a real number θ, its angle in radians from the positive x-axis.
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