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Unformatted text preview: ) = 2 as 2 cos x + π = 2,
or cos x + π = 1. Solving the latter, we get x = − π + 2πk for integers k . Only one of these
solutions, x = 53 , which corresponds to k = 1, lies in [0, 2π ). Geometrically, we see that
y = cos(x) − 3 sin(x) and y = 2 intersect just once, supporting our answer. y = sin(x) cos x
2 + cos(x) sin x
2 and y = 1 y = cos(x) − √ 3 sin(x) and y = 2 We repeat here the advice given when solving systems of nonlinear equations in section 8.7 – when
it comes to solving equations involving the trigonometric functions, it helps to just try something.
8 We are essentially ‘undoing’ the sum / diﬀerence formula for cosine or sine, depending on which form we use, so
this problem is actually closely related to the previous one! 10.7 Trigonometric Equations and Inequalities 737 Next, we focus on solving inequalities involving the trigonometric functions. Since these functions
are continuous on their domains, we may use the sign diagram technique we’ve u...
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