Vectors and the trigonometric function

In summary, The question involves two vectors with magnitudes of 10 and 15, with an angle of 65 degrees between them. The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors, can be solved using trigonometric functions. The answer is approximately 13.6.
  • #1
nath_quam
13
0
Hey I'm just having trouble with this question

Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65 deg. The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors, is:

a)0
b)4.2
c)9.1
d)13.6
e)6.3

Thanks Nath
 
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  • #2
dear Nath , i think you can solve it by trigonometric function.

which step you are not clear,or you just can't sure whether the right answer is in the abcde.
 
  • #3
i'm unsure where to start

Nath
 
  • #4
i just worked it out...i sketched the picture and used trigonometry

sin65° = x/15

Therefore: .x = 15·sin65° ≈ 13.6
 
  • #5
clever guy. i knew you can do it
 

Related to Vectors and the trigonometric function

1. What are vectors and how are they used in trigonometric functions?

Vectors are mathematical quantities that have both magnitude and direction. They are commonly represented by arrows in two or three-dimensional space. In trigonometric functions, vectors are used to describe the magnitude and direction of forces, velocities, and other quantities that involve direction.

2. What is the relationship between vectors and the trigonometric functions sine, cosine, and tangent?

The sine, cosine, and tangent functions are trigonometric functions that relate the angles of a right triangle to the lengths of its sides. Vectors can be used to represent the sides of a right triangle, and the cosine, sine, and tangent of an angle can be calculated using vector operations.

3. How do you find the magnitude and direction of a vector using trigonometric functions?

To find the magnitude of a vector, you can use the Pythagorean theorem, which involves the sine, cosine, and tangent functions. The direction of a vector can be found using the inverse tangent function, also known as arctangent, which gives the angle of the vector in relation to the positive x-axis.

4. Can vectors and trigonometric functions be applied in real-world situations?

Yes, vectors and trigonometric functions have many real-world applications. For example, in physics, vectors are used to describe the velocity and acceleration of an object, and trigonometric functions are used to calculate the forces acting on the object. In engineering, vectors and trigonometric functions are used to design structures and calculate forces and stresses.

5. Are there any other trigonometric functions related to vectors?

Yes, there are other trigonometric functions that are related to vectors, such as the secant, cosecant, and cotangent. These functions are inverses of the cosine, sine, and tangent functions, respectively. They can also be used to calculate the magnitude and direction of a vector.

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