Vector Components and Trigonometric Functions

The video tutorial by Mark Heredos on MathGuide.com explains vectors, which have both magnitude and direction. It covers how to break vectors into horizontal and vertical components, particularly useful in fields like engineering and physics. The tutorial demonstrates calculating these components using trigonometry, specifically cosine and sine functions, and concludes with practical applications of these concepts.

What is a vector characterized by?

• Neither magnitude nor direction

• Magnitude and direction

• Only direction

• Only magnitude

Which of the following is NOT a vector?

• A force of 120 Newtons at a 35° angle

• A skateboard moving south at 3 mph

• A car traveling at 60 mph

• A plane flying north at 500 mph

Why do engineers and physicists break vectors into components?

• To change the direction

• To simplify calculations

• To increase the magnitude

• To eliminate the vector

What is the first step in breaking a vector into components?

• Calculate the magnitude

• Draw a coordinate system

• Find the resultant vector

• Determine the vector's color

Which trigonometric function is used to find the horizontal component of a vector?

• Secant

• Cosine

• Tangent

• Sine

If a vector has a magnitude of 120 Newtons and an angle of 35°, what is the horizontal component approximately?

• 120 Newtons

• 35 Newtons

• 68.83 Newtons

• 98.30 Newtons

Which trigonometric function is used to find the vertical component of a vector?

• Cotangent

• Tangent

• Sine

• Cosine

What is the approximate vertical component of a vector with a magnitude of 120 Newtons and an angle of 35°?

• 35 Newtons

• 120 Newtons

• 68.83 Newtons

• 98.30 Newtons

Why is it useful to break vectors into horizontal and vertical components?

• To eliminate the vector

• To simplify the addition of vectors

• To change the vector's direction

• To change the vector's magnitude

What is the final step after calculating the components of a vector?

• Add the components

• Multiply the components

• Subtract the components

• Divide the components