Solving precalc problem without calculator

In summary, to find the value of sec theta when the terminal side of angle theta in standard position passes through (-2,-3), you can use the Pythagorean theorem to find the length of the third side of a triangle with vertices at (0,0), (-2,-3), and (-2,0). Alternatively, you can use the circular definition of sine and cosine to find the x-coordinate of a point on the line passing through (-2,-3) that intersects the unit circle, and then find 1/cosine to get the value of sec theta.
  • #1
bfpri
12
0
The terminal side of an angle theta in standard position passes through (-2,-3). What is sec theta?

How would you solve this problem without a calculator?

Thanks.
 
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  • #2
One approach to start with is draw this angle on a cartesian coordinate system, maybe including in the form of a triangle; you may need to express something using pythagorean theorem. Remember that 1/(cosine) = secant.
 
  • #3
you could set up a triangle having (0,0) as one vertex, (-2, -3) as another and (-2, 0) as the third. What are the lengths of the three sides? What is sec of the angle at the origin (which is what you must mean by "theta"- you didn't specify what "theta" was!). Remember that these are "signed" lengths. Distances measured downward or to the left are negative.

Even simpler would be to use the "circular" definition of sine and cosine: Draw a unit circle. Starting at (1, 0) measure around the circumference a distance t. The coordinates of the end point are, by definition, (cos t, sin t). Now, (-2, -3) does not lie on the unit circle but it is easy to find a point on that line that does (use "similar triangles"). What is the x coordinate of that point? What is 1/cosine?
 

1. How can I solve precalc problems without a calculator?

To solve precalc problems without a calculator, you need to have a good understanding of the fundamental concepts and formulas in precalculus. This includes knowing basic arithmetic, algebraic manipulation, trigonometric identities, and geometric principles. With practice and familiarity, you can develop mental math techniques to solve problems efficiently without a calculator.

2. Is it necessary to solve precalc problems without a calculator?

No, it is not necessary to solve precalc problems without a calculator. However, it can be a useful skill to have and can improve your problem-solving abilities. Additionally, some exams or tests may not allow the use of a calculator, so being able to solve problems without one can be beneficial.

3. How can I improve my mental math skills for precalc?

To improve your mental math skills for precalc, it is important to practice regularly. Start with simple problems and gradually work your way up to more complex ones. You can also use flashcards or online resources to test your skills and identify areas for improvement. Additionally, try to understand the underlying concepts rather than just memorizing formulas, as this will help you solve problems more efficiently.

4. Are there any tips for solving precalc problems without a calculator?

Yes, there are a few tips that can help you solve precalc problems without a calculator. One tip is to break down the problem into smaller, more manageable parts. Another is to estimate the answer before solving the problem to check if your final answer is reasonable. You can also use shortcuts or mental math tricks, such as multiplying by powers of 10 or using patterns in numbers.

5. Can I use a calculator for some parts of a precalc problem?

Yes, you can use a calculator for certain parts of a precalc problem, such as basic arithmetic calculations or finding decimal approximations. However, it is important to understand the concepts and formulas being used and not rely solely on the calculator. Also, on exams or tests, make sure to follow any guidelines or restrictions on calculator usage.

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