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Trigonometry Intro - PhysPrimer
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Some basic applications of trigonometry in converting between describing a vector in terms of its magnitude and direction (hypotenuse and angle) and its x and y components (adjacent and opposite sides).
0:00 Introduction (vectors and right angle triangles)
3:01 Make sure calculator is in right mode (deg vs rad)
3:55 Pythagoras Theorem and trig function definitions
5:01 Example 1 (Hypotenuse and angle to opposite and adjacent sides)
8:45 Calculation check (which side length should be greater?)
10:00 Example 2a (Opposite and adjacent sides to hypotenuse and angle)
12:00 Calculation check (Hypotenuse should be longest side)
12:13 Example 2b (Finding the angle)
15:32 Calculation check (Is angle more or less than 45 degrees?)
17:07 Uses with other vectors
20:48 Try it yourself examples (solutions at end of description)
Opening Image Credit: NASA, ESA, CSA, STScI, Klaus Pontoppidan (STScI), Image Processing: Alyssa Pagan (STScI)
Solutions to "Try it yourself" examples (and I do recommend trying these yourself BEFORE looking at solution):
1) For 150N force:
x-component is -127.2N (negative because this vector is pointing partially to the left and the +x direction points to the right)
y-component is +79.5N (positive because this vector is pointing partially upwards and the +y direction points up)
2) For magnetic field vector:
Magnitude (hypotenuse) = 51.9uT (be careful when applying Pythagoras theorem with the negative component... when you square that negative component, the result is positive, and the hypotenuse should always be the longest side of the triangle)
Angle = 64.9 degrees below +x axis (some conventions count angles measured clockwise to be negative; I generally write the angles in this way for clarity since we might not always be measuring the angle from the +x axis as well)
0:00 Introduction (vectors and right angle triangles)
3:01 Make sure calculator is in right mode (deg vs rad)
3:55 Pythagoras Theorem and trig function definitions
5:01 Example 1 (Hypotenuse and angle to opposite and adjacent sides)
8:45 Calculation check (which side length should be greater?)
10:00 Example 2a (Opposite and adjacent sides to hypotenuse and angle)
12:00 Calculation check (Hypotenuse should be longest side)
12:13 Example 2b (Finding the angle)
15:32 Calculation check (Is angle more or less than 45 degrees?)
17:07 Uses with other vectors
20:48 Try it yourself examples (solutions at end of description)
Opening Image Credit: NASA, ESA, CSA, STScI, Klaus Pontoppidan (STScI), Image Processing: Alyssa Pagan (STScI)
Solutions to "Try it yourself" examples (and I do recommend trying these yourself BEFORE looking at solution):
1) For 150N force:
x-component is -127.2N (negative because this vector is pointing partially to the left and the +x direction points to the right)
y-component is +79.5N (positive because this vector is pointing partially upwards and the +y direction points up)
2) For magnetic field vector:
Magnitude (hypotenuse) = 51.9uT (be careful when applying Pythagoras theorem with the negative component... when you square that negative component, the result is positive, and the hypotenuse should always be the longest side of the triangle)
Angle = 64.9 degrees below +x axis (some conventions count angles measured clockwise to be negative; I generally write the angles in this way for clarity since we might not always be measuring the angle from the +x axis as well)
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