217k views
4 votes
Write the vector described below in component form. Magnitude = 70

Amplitude (degree measure) = 104°

User Evilsanta
by
7.2k points

1 Answer

1 vote

Final answer:

The vector with a magnitude of 70 and an amplitude of 104° can be written in component form using trigonometry, with the x-component calculated as 70 × cos(104°) and the y-component as 70 × sin(104°). The exact component values should be calculated depending on the use of degrees or radians.

Step-by-step explanation:

To write the vector with a magnitude of 70 and an amplitude of 104° in component form, we use trigonometry. The x-component (horizontal) can be found using the cosine of the angle, and the y-component (vertical) using the sine:

  • Ax = 70 × cos(104°)
  • Ay = 70 × sin(104°)

Note that since the angle is more than 90° but less than 180°, the x-component will be negative because it is in the second quadrant, where cosines are negative.

The vector in component form is then <Ax, Ay>, where:

  • Ax = 70 × cos(104°) (calculate the exact value depending on whether you want to use degrees or radians for the angle measure)
  • Ay = 70 × sin(104°) (again, calculate the exact value accordingly)

User Garrow
by
7.9k points