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Stitz-Zeager_College_Algebra_e-book

# We dened the cartesian coordinate plane using two

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Unformatted text preview: onsist of the intervals π + πk, π + πk = 4 express our ﬁnal answer as (4k+1)π , (k 4 ∞ k=−∞ + 1)π . Using extended interval notation, we (4k + 1)π , (k + 1)π 4 742 Foundations of Trigonometry 10.7.1 Exercises 1. Find all of the exact solutions to each of the following equations and then list those solutions which are in the interval [0, 2π ). (a) sin (5x) = 0 1 (b) cos (3x) = 2 (c) tan (6x) = 1 π 1 =− 3 2 √ 7π (j) 2 cos x + =3 4 (d) csc (4x) = −1 √ (e) sec (3x) = 2 √ (k) tan (2x − π ) = 1 3 (f) cot (2x) = − √3 2 x (g) sin = 3 2 5π =0 (h) cos x + 6 (i) sin 2x − (l) tan2 (x) = 3 4 3 1 (n) cos2 (x) = 2 3 (o) sin2 (x) = 4 (m) sec2 (x) = 2. Solve each of the following equations, giving the exact solutions which lie in [0, 2π ) (a) sin (x) = cos (x) (k) sin(6x) cos(x) = − cos(6x) sin(x) (b) sin (2x) = sin (x) (l) cos(2x) cos(x) + sin(2x) sin(x) = 1 (c) sin (2x) = cos (x) (d) cos (2x) = sin (x) (e) cos (2x) = cos (x) (f) tan3 (x) = 3 tan (x) 3 (g) tan2 (x) = sec (x) 2 (h) cos3 (x) = − cos (x) √ (m) cos(5x) cos(3x) − sin(5x) sin(3x) = 3...
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