Can Someone Explain This Trig Picture to Me?

In summary, the conversation discusses the use of the dot product and trigonometry to find projections onto different axes. The formula for the dot product is used to find the projection of r onto x and y axes, while the formula for phi is used to find the projection of phi onto x and y axes. However, there is confusion about why the last projection, phi (dot) y, results in a positive value for cosine instead of a negative value.
  • #1
Meadman23
44
0
Its the attached picture. I'm not seeing why when using the dot product, they start using sin.
 

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  • #2
The picture is self explanatory. If you know trig, it should be elementary.
 
  • #3
Projections onto different axes.
 
  • #4
I'm just not getting it. '
I see that the angle between r and x is phi, thus in using the formula, r (dot) x = (1)(1) cos(phi).

Then I see the angle between r and y is (90-phi), thus in using the formula, r (dot) y = (1)(1)cos(90-phi) = sin (phi).

I then see the angle between phi and x is (90 +phi), thus in using the formula, phi (dot) x = (1)(1)cos(90+phi) = -sin (phi)

I then see the angle between phi and y is (180 - phi), thus in using the formula, phi (dot) y = (1)(1)cos(180-phi) = -cos (phi)?

I don't get why the last one is +cos(phi)...
 
  • #5
Look at the blue part of the diagram ... phi(dot)y = cos(phi).
 

1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving right triangles and is important in fields such as physics, engineering, and navigation.

2. What is a trigonometric function?

A trigonometric function is a mathematical function that relates the angles of a triangle to the lengths of its sides. Examples of trigonometric functions include sine, cosine, and tangent.

3. What is the purpose of using a trigonometric picture?

A trigonometric picture, also known as a unit circle, is used to visualize the relationships between the angles and sides of a right triangle. It helps to understand the concepts and applications of trigonometry in a visual way.

4. How do you read a trigonometric picture?

In a trigonometric picture, the angle is represented by a point on the unit circle and the radius of the circle represents the hypotenuse of a right triangle. The coordinates of the point correspond to the values of the trigonometric functions for that angle.

5. Why is trigonometry important in real life?

Trigonometry is used in various real-life applications, such as architecture, surveying, navigation, and engineering. It helps to solve problems involving angles and distances, and is also used in fields such as physics, astronomy, and geography.

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