Stitz-Zeager_College_Algebra_e-book

# If we are asked for an arccotangent arcsecant or

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Unformatted text preview: e < θ < π 2 (c) tan(θ) = 3 π 12 3π 16. If sin(α) = where 0 < α < and cos(β ) = where < β < 2π , ﬁnd the exact values 5 2 13 2 of the following. (a) sin(α + β ) (b) cos(α − β ) (c) tan(α − β ) π 24 3π 5 where π < β < , ﬁnd the exact values 17. If sec(α) = − where < α < π and tan(β ) = 3 2 7 2 of the following. (a) csc(α − β ) (b) sec(α + β ) (c) cot(α + β ) 1 18. Let θ be a Quadrant III angle with cos(θ) = − . Show that this is not enough information to 5 θ 7π 3π determine the sign of sin by ﬁrst assuming 3π < θ < and then assuming π < θ < 2 2 2 θ and computing sin in both cases. 2 √ √ √ 2+ 3 6+ 2 19. Without using your calculator, show that = 2 4 20. Drawing on part 4 of Example 10.4.3 for inspiration, write cos(4θ) as a polynomial in cosine. Then write cos(5θ) as a polynomial in cosine. Can you ﬁnd a pattern so that cos(nθ) could be written as a polynomial in cosine for any natural number n? 670 Fou...
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