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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 92 (page 487)

solve each equation on the interval
$\sqrt{3} \sin 胃 + \cos 胃 = 1$

Short Answer

Expert verified

$胃 = n 蟺 + {(- 1)}^{n} \frac{蟺}{6} - \frac{蟺}{6}$

Step by step solution

01

Step 1.Given information is

a trignometirc equation $\sqrt{3} \sin 胃 + \cos 胃 = 1$

02

Step 2. Multiplying both the side by 12

$\frac{\sqrt{3}}{2} \sin 胃 + \frac{1}{2} \cos 胃 = \frac{1}{2} \cos (\frac{蟺}{6}) \sin 胃 + \sin (\frac{蟺}{6}) \cos 胃 = \sin (\frac{蟺}{6}) \sin (胃 + \frac{蟺}{6}) = \sin (\frac{蟺}{6})$

03

Step 3.The general solution we get is

$胃 = n 蟺 + {(- 1)}^{n} \frac{蟺}{6} - \frac{蟺}{6}$

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Most popular questions from this chapter

If $\tan 伪 = x + 1$ and role="math" localid="1646425111199" $\tan 尾 = x - 1,$ show that

role="math" localid="1646426027733" $2 c o t (伪 - b) = x^{2}$

Establish each identity.

$\frac{1}{1 - \sin 胃} + \frac{1}{1 + \sin 胃} = 2 s e c^{2} 胃$

Show that $\sin (\sin^{- 1} (v) + \cos^{- 1} (v)) = 1$

Suppose that f and g are two functions with the same domain. If $f (x) = g (x)$ for every x in the domain, the equation is called a(n) ____. Otherwise, it is called a(n) _____ equation.

Establish each identity.

$\frac{{(2 \cos^{2} 胃 - 1)}^{2}}{\cos^{4} 胃 - \sin^{4} 胃} = 1 - 2 \sin^{2} 胃$

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