Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
You did ask for the EXACT value, which no one has posted yet. The exact value is √(2 + √3)/2. To three decimal places, that is .966.
As for how I got that, I started with a 30-60-90 triangle and extended the longer side by the length of the hypotenuse to get a 15-75-90 triangle, then used Pythagoragus. For some reason, though, most students have an easier time using a half-angle formula, so feel free to do it that way.
* * * *
OK, sorry, I see Awesome Sauce also gives an exact value. It is also correct, just looks a little different.
* * * *
From your comment in Additional Details, it appears you want to use the angle difference relation: cos(π/12) = cos(π/4 - π/6). That works also, but you need to get the formula right, which is:
cos(a - b) = cos a * cos b + sin a * sin b
For cos (45 - 30), this gives cos 45 * cos 30 + sin 45 * sin 30 = √2/2 * √3/2 + √2/2 * 1/2 = √2/4(√3 + 1). This is yet another expression for the same exact value.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
