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ss_5_2 - Section 5.2 Trigonometric Functions There are six...

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Section 5.2 Trigonometric Functions There are six basic trigonometric functions: sine , cosine , tangent , cosecant , secant , cotangent . In this section, we introduce and deﬁne these six functions. We begin by deﬁning the trig functions for acute angles, and then we extend the deﬁnitions to all angles, using the unit circle method. We also show how to evaluate trig functions of arbitrary angles using reference angles. Acute Triangle Approach For acute angles, we deﬁne the six trigonometric functions of the angles as follows: sin A = a c cos A = b c tan A = a b = sin A cos A csc A = c a = 1 sin A sec A = c b = 1 cos A cot A = b a = cos A sin A = 1 tan A Unit Circle Approach For angles that are not acute, we use the unit circle approach to deﬁne the six trigonometric functions as follows: sin θ = b cos θ = a tan θ = b a = sin θ cos θ csc θ = 1 b = 1 sin θ sec θ = 1 a = 1 cos θ cot θ = a b = 1 tan θ = cos θ sin θ Note that the above shows that all of the trig functions can be deﬁned in terms of the sine and cosine. 1

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Reference Angle Approach The diagram shown below gives the reference angles for all four quadrants. Reference angles are always acute angles, and the value of a trig function for any angle
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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ss_5_2 - Section 5.2 Trigonometric Functions There are six...

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