THE COMPOUND // FIELD NOTES // WEEK 11
Abstract equations, unit multipliers, and first trig
Field Book
Lessons 40 to 43
Due
Test 9 due ยท Supplement 11
Method
Paper first, every step
Lesson 42 states the year's motto: never estimate, always calculate. Sine, cosine, and tangent report for duty.
What you have to be able to do
- Solve abstract fractional equations for a chosen variable
- Convert measures with unit multipliers
- Use sine, cosine, and tangent ratios and their inverses
The procedures
Abstract fractional equationsField Book Lesson 40
- Clear fractions with the LCD exactly as with numbers.
- Collect every term containing the target variable, factor it out, divide.
Unit multipliersField Book Lesson 41
- Multiply by a fraction equal to 1 whose units cancel the old and install the new.
- Chain multipliers for multi-step conversions and cancel units like factors.
Calculate, do not estimateField Book Lesson 42
- Scientific notation problems get computed exactly, then rounded at the end.
- Never round in the middle of the work.
Sine, cosine, tangentField Book Lesson 43
- In a right triangle: sin is opposite over hypotenuse, cos is adjacent over hypotenuse, tan is opposite over adjacent.
- The inverse functions recover the angle from the ratio.
Worked: feet to inches
- Convert 3 feet to inches with a unit multiplier.
- 3 ft times 12 in1 ft: the feet cancel.
- 3 times 12 = 36 inches.
Terms on the record
| Term | Meaning |
|---|
| unit multiplier | a fraction equal to one used to convert units |
| sine | in a right triangle, opposite over hypotenuse |
| inverse function | the function that recovers the input from the output |