Dude told me to post them seperately, so...
find exact value of
cos(2 arcsin(1/4))
How can i do it?
The thing was HOW DO I DO IT WITHOUT A CALCULATOR? Hence the words, "how can I do it?"
I would like to know how to do it without a calculator, considering I will have to do problems like it on the final tomorrow. So stop saying to use a calculator! Please, if you're going to say for me to use a calculator, then please do not answer!
find exact value of
cos(2 arcsin(1/4))
How can i do it?
The thing was HOW DO I DO IT WITHOUT A CALCULATOR? Hence the words, "how can I do it?"
I would like to know how to do it without a calculator, considering I will have to do problems like it on the final tomorrow. So stop saying to use a calculator! Please, if you're going to say for me to use a calculator, then please do not answer!
-
cos(2 arcsin(1/4))
Replace: arcsin(1/4) = A
Cos 2A = (cos A)^2 - (sin A)^2
sin A = sin arcsin 1/4 = 1/4 (easy right?)
(cos A)^2 = 1 - (sin A)^2 = 1 - (sin arcsin 1/4)^2 = 1 - (1/4)^2 = 1 - 1/16 = 15/16
Cos 2A = (cos A)^2 - (sin A)^2 = 15/16 - (1/4)^2 = 15/16 - 1/16 = 14/16 = 7/8
cos(2 arcsin(1/4)) = 7/8
Well, you still need a calculator to calculate 7/8 :)))
Replace: arcsin(1/4) = A
Cos 2A = (cos A)^2 - (sin A)^2
sin A = sin arcsin 1/4 = 1/4 (easy right?)
(cos A)^2 = 1 - (sin A)^2 = 1 - (sin arcsin 1/4)^2 = 1 - (1/4)^2 = 1 - 1/16 = 15/16
Cos 2A = (cos A)^2 - (sin A)^2 = 15/16 - (1/4)^2 = 15/16 - 1/16 = 14/16 = 7/8
cos(2 arcsin(1/4)) = 7/8
Well, you still need a calculator to calculate 7/8 :)))