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0. Review of College Algebra(0)

Rationalizing Denominators
(0)

Pythagorean Theorem & Basics of Triangles
(0)

Basics of Graphing
(0)

Functions
(0)

Transformations
(0)

Asymptotes
(0)

Solving Linear Equations
(0)

Solving Quadratic Equations
(0)

Complex Numbers
(0)

1. Measuring Angles(0)

Angles in Standard Position
(0)

Coterminal Angles
(0)

Complementary and Supplementary Angles
(0)

Radians
(0)

2. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
(0)

Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

3. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
(0)

Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

4. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

5. Inverse Trigonometric Functions and Basic Trigonometric Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

6. Trigonometric Identities and More Equations(0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

7. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

8. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

9. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

10. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

11. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

8. Vectors

Direction of a Vector

8. Vectors

Direction of a Vector: Videos & Practice Problems

Video Lessons Practice Worksheet

Direction of a Vector Practice Problems

20 problems

Problem 1Multiple Choice

Find the magnitude and direction angle of the vector a given below. Express your answer to one decimal place.

$a = 12i - 18j$

Problem 2Multiple Choice

Find the magnitude and direction angle of the vector a given below. Express your answer to one decimal place.

$a=(31i-17j)-(25i-17j)$

Problem 3Multiple Choice

For the given vector, calculate its magnitude and direction angle relative to the positive $x$ -axis. Express your answer to the nearest tenth, if required.

$〈-17,-29〉$

Problem 4Multiple Choice

For the given vector, calculate its magnitude and direction angle. Express your answer to the nearest tenth, if required.

$〈-16,63〉$

Problem 5Multiple Choice

For the given vector, calculate its magnitude and direction angle. Express your answer to the nearest tenth, if required.

$〈28\sqrt3,-28\sqrt3〉$

Problem 6Multiple Choice

A vector has components of x = 3 and y = 4. What is the direction of this vector in degrees, measured from the positive x-axis?

Problem 7Multiple Choice

Which trigonometric function can be used to define the direction of a vector based on its x and y components?

Problem 8Multiple Choice

A vector lies in the third quadrant with an angle calculated as 30 degrees from the negative x-axis. What is the positive angle of this vector from the positive x-axis?

Problem 9Multiple Choice

If the opposite side of a right triangle is 5 units and the hypotenuse is 13 units, what is the sine of the angle opposite to the 5-unit side?

Problem 10Multiple Choice

A vector makes an angle of 45 degrees with the negative y-axis in the second quadrant. What is its positive angle from the positive x-axis?

Problem 11Multiple Choice

A vector has a magnitude of 10 units and points at an angle of 60 degrees from the positive x-axis. What are the x and y components of this vector?

Problem 12Multiple Choice

What are the x and y components of a vector with a magnitude of 1 unit and a direction of π/4 radians?

Problem 13Multiple Choice

A vector has components x = -3 and y = 4. Which quadrant does this vector lie in, and what does this imply about its direction?

Problem 14Multiple Choice

If a vector has components x = 6 and y = -8, what are the magnitude and direction of this vector?

Problem 15Multiple Choice

An airplane is flying with a velocity vector that has a magnitude of 500 km/h at an angle of 30 degrees east of north. What are the northward and eastward components of the airplane's velocity?

Problem 16Multiple Choice

Which mnemonic device is used to remember the relationships between the sides of a right triangle and its angles when using sine, cosine, and tangent?

Problem 17Multiple Choice

A vector has components of x = -5 and y = 5. What is the direction of this vector in degrees, measured counterclockwise from the positive x-axis?

Problem 18Multiple Choice

A vector with a magnitude of 15 units points at an angle of 120 degrees from the positive x-axis. What are the x and y components of this vector?

Problem 19Multiple Choice

If a vector has components x = -4 and y = -3, what are the magnitude and direction of this vector from the positive x-axis?

Problem 20Multiple Choice

A river flows with a velocity vector that has a magnitude of 3 m/s directed 45 degrees south of east. What are the southward and eastward components of the river's velocity?