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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. 18 (page 485)

Find the exact value of the expression:
$\tan 195^{掳}$

Short Answer

Expert verified

$(\frac{3 鈭� \sqrt{3}}{3 + \sqrt{3}})$

Step by step solution

01

Step 1. Given information

We have been given an expression $\tan 195^{掳}$ .

We have to find its exact value.

02

Step 2. Simplify the expression

We can also write the expression as:

$\tan 190^{掳} = \tan (150^{掳} + 45 掳)$

03

Step 3. Apply the compound angle formula

$\tan (150^{掳} + 45 掳)$ has the form $\tan (伪 + 尾)$

Therefore, apply

$\tan (伪 + 尾) = \frac{\tan 伪 + \tan 尾}{1 - + \tan 伪 \tan 尾}$

$\begin{aligned} \frac{\tan 鈦� (150^{鈭�}) + \tan 鈦� (45^{鈭�})}{1 鈭� \tan 鈦� (150^{鈭�}) \tan 鈦� (45^{鈭�})} = \frac{鈭� (\frac{\sqrt{3}}{3}) + 1}{1 鈭� (鈭� (\frac{\sqrt{3}}{3}))} \\ = \frac{(\frac{3}{3}) 鈭� (\frac{\sqrt{3}}{3})}{(\frac{3}{3}) + (\frac{\sqrt{3}}{3})} \\ = \frac{(\frac{3 鈭� \sqrt{3}}{3})}{(\frac{3 + \sqrt{3}}{3})} \\ = (\frac{3 鈭� \sqrt{3}}{3 + \sqrt{3}}) \end{aligned}$

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Most popular questions from this chapter

Establish each identity.

$\frac{\sin^{3} 胃 + \cos^{3} 胃}{1 - 2 \cos^{2} 胃} = \frac{s e c 胃 - \sin 胃}{\tan 胃 - 1}$

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

solve each equation on the interval $0 鈮� 胃 < 2 蟺$

$\sin 胃 - \sqrt{3} \cos 胃 = 1$

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.

$\frac{\sin^{3} 胃 + \cos^{3} 胃}{\sin 胃 + \cos 胃} = 1 - \sin 胃 \cos 胃$

See all solutions

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