Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

8. Vectors

Geometric Vectors

Trigonometry

8. Vectors

Geometric Vectors

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In Exercises 5–12, sketch each vector as a position vector and find its magnitude.v = -4i

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Open Question

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

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Open Question

Find the angle between the vectors. Round to the nearest tenth of a degree. If the vectors are orthogonal, say so.

〈5, -3〉, 〈3, 5〉

Open Question

Solve each problem. See Examples 5 and 6.

Distance and Direction of a Motorboat A motorboat sets out in the direction N 80° 00′ E. The speed of the boat in still water is 20.0 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.

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Open Question

In Exercises 5–12, sketch each vector as a position vector and find its magnitude.v = -6i - 2j

Open Question

In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.P₁ = (-4, -4), P₂ = (6, 2)

Open Question

In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.P₁ = (-8, 6), P₂ = (-2, 3)

Open Question

In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.P₁ = (-1, 7), P₂ = (-7, -7)

Open Question

In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.P₁ = (-3, 4), P₂ = (6, 4)

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