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Description: Solve 6 sin(z) = 2 for the four smallest positive solutionsGive your answers in radians and accurate to at least two decimal places, as a list separated by commas

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Calculus

Solve 6 sin(z) = 2 for the four smallest positive solutions Give your answers in radians and accurate to at least two decimal places, as a list separated by commas

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.4: Multiple-angle Formulas

Problem 72E

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Concept explainers

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

Topic Video

Question

Solve 6 sin(z) = 2 for the four smallest positive solutions
Give your answers in radians and accurate to at least two decimal places, as a list separated by commas

Expert Solution

Step 1

Given equation is

$6 \sin (\frac{π}{3} x) = 2$

We need to solve for $x$ .

Step 2

$We have \sin (x) = a \Rightarrow x = \sin^{- 1} (a) + 2 πn and x = π - \sin^{- 1} (a) + 2 πn$

Therefore, we get

$For 6 \sin (\frac{π}{3} x) = 2 \sin (\frac{π}{3} x) = \frac{1}{3} \Rightarrow \frac{πx}{3} = s i n^{- 1} (\frac{1}{3}) + 2 πn and \frac{πx}{3} = π - s i n^{- 1} (\frac{1}{3}) + 2 πn n \in ℤ \Rightarrow x = \frac{3}{π} s i n^{- 1} (\frac{1}{3}) + 6 n and x = 3 - \frac{3}{π} s i n^{- 1} (\frac{1}{3}) + 6 n n \in ℤ$

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