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Unformatted text preview: 0.3 The Six Circular Functions and Fundamental Identities 10.3 635 The Six Circular Functions and Fundamental Identities In section 10.2, we defined cos(θ) and sin(θ) for angles θ using the coordinate values of points on the Unit Circle. As such, these functions earn the moniker circular functions. It turns out that cosine and sine are just two of the six commonly used circular functions which we define below. Definition 10.2. The Circular Functions: Suppose θ is an angle plotted in standard position and P (x, y ) is the point on the terminal side of θ which lies on the Unit Circle. • The cosine of θ, denoted cos(θ), is defined by cos(θ) = x. • The sine of θ, denoted sin(θ), is defined by sin(θ) = y . • The secant of θ, denoted sec(θ), is defined by sec(θ) = 1 , provided x = 0. x • The cosecant of θ, denoted csc(θ), is defined by csc(θ) = 1 , provided y = 0. y y , provided x = 0. x x • The cotangent of θ, denoted cot(θ), is defined by cot(θ) = , provided y = 0. y • The tangent of θ, denoted tan(θ), is de...
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