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	Precalculus Functions and Graphs 4/e Barnett/Ziegler/Byleen
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Chapter 7: Additional Topics in Trigonometry

Worked Exercises

Chapter 7: Additional Topics in Trigonometry

Exercise Set 7-1

Solve the triangle.

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Solve the triangle. If there is no solution, say so.

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APPLICATIONS

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Exercise Set 7-2

The law of sines or the law of cosines is involved. Solve the triangle. If there is no solution, say so.

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APPLICATIONS

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Exercise Set 7-3

Figures (a) and (b) show vector addition for vectors u and v at right angles to each other. Find |u + v| and , given |u| and |v| in figures (a) and (b).

Solution

Find |u| and |v|, the magnitudes of the horizontal and vertical components of u + v, given |u + v| and in figures (a) and (b).

Solution

Find |u + v| and alpha, given |u|, |v|, and in figures (a) and (b).

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Find |u| and |v|, given |u + v|, > and in figures (a) and (b).

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Exercise Set 7-4

Represent the geometric vector AB, with endpoints as indicated, as an algebraic vector in the form (a, b).

Solution

Find the magnitude of the vector.

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Find: (A) u + v
(B) u - v
(C) 2u - v + 3w

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Express v in terms of the i and j unit vectors.

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Let u = 3i - 2j, v = 2i + 4j, and w = 2i, and perform the indicated operations.

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Find the unit vector u with the same direction as v.

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Let u = < a, b >, v = < c, d >, and w = < e, f > be vectors and m and n be scalars. Prove the following vector properties using appropriate properties of real numbers and the definitions of vector addition and scalar multiplication.

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Exercise Set 7-5

Plot A, B and C in a polar coordinate system.

Solution

Graph the expression in a polar coordinate system.

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Convert the polar coordinates to rectangular coordinates to three decimal places.

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Convert the rectangular coordinatews to polar coordinates with in degree measure, -180° < < 180°, and R < 0.

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Change the rectangular equation to polar form.

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Exercise Set 7-6

Plot the set of complex numbers in a complex plane.

Solution

Change into polar form. Choose in degrees, -180° < <= 180°. Compute the modulus and arguments for part A and B exactly, and for part C to two decimal places.

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Change parts A-C to rectangular form. Compute the exact values for parts A and B; compute a and b for a + bi to two decimal places.

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Find z₁z₂ and z₁/z₂.

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Simplify directly and by using polar forms. Write the answer in both rectangular and polar forms, in degrees.

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Exercise Set 7-7

Use De Moivre's theorem to evaluate the expression. Leave the answer in polar form.

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Find the value of the expression and write the final answer in exact rectangular form.

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For n and z find all nth roots of z. Leave the answer in polar form.

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For n and z find all nth roots of z. Write the answer in polar form, and plot in a complex plane.

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Solve the equation for all roots. Write the final answer in polar abd exact rectangular form.

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Write the answer in polar form.

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