Finding Exact Value of Cos A: Solutions Requested

In summary, to find the exact value of cosA from the equation secA-cosA=1/2, you can make the substitution cosA=x and use the definition of secant to get a quadratic equation in x. Then, solve for x and use inverse cosine to find the value of A. Alternatively, you can multiply everything by cosA to get a quadratic equation in cosA and solve using the quadratic formula.
  • #1
bob4000
40
0
i and the rest of my class are finding it impossible to find the answer to this part of the question:

find the exact value of cos A from secA-cosA=1/2

thanks in advance
 
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  • #2
Make the substitution [itex] \cos A =x [/itex], then the definition of secant and in the end you should get a quadratic equation in "x".

Daniel.
 
  • #3
What you do is that you multiply everything by cosA, so that you get a quadratic, and then solve that in terms of cosA, to get A, simply inverse cos it, eg

(1/cosA) - cosA = 1/2
-cos^2A + 1 = (1/2)cosA
0 = cos^2A + 0.5cosA -1
Then solve with the quadratic formula:biggrin:

edit: dam,beaten to it...
 
  • #4
merci beaucoup
 

Related to Finding Exact Value of Cos A: Solutions Requested

1. What is the definition of cos A?

Cos A is a mathematical function that represents the ratio of the adjacent side to the hypotenuse in a right triangle, where A is the angle between the adjacent side and the hypotenuse.

2. How do I find the exact value of cos A?

To find the exact value of cos A, you can use a scientific calculator or a trigonometric table. Alternatively, you can use the cosine function in a programming language such as Python or Java.

3. Can I find the exact value of cos A without a calculator?

Yes, you can find the exact value of cos A without a calculator by using trigonometric identities and formulas, such as the Pythagorean identity or the double angle formula.

4. Why is it important to find the exact value of cos A?

Finding the exact value of cos A is essential in many fields such as engineering, physics, and astronomy, where precise calculations are necessary. It also helps in understanding the properties and behavior of trigonometric functions.

5. What are some common mistakes when finding the exact value of cos A?

Some common mistakes when finding the exact value of cos A include using the wrong formula, inputting the incorrect angle measure, and not converting the angle measure to the appropriate unit. It's essential to double-check your calculations and use the correct formula for the given problem.

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