Hello all,
Currently, we are covering the trigonometric identities (half-angle, sum, difference, etc.). One particular problem asked to solve for the sin(195deg). So, I first attempted with the sum formula, splitting the 195 into 150 and 45. This yielded the result (sqrt(2) - sqrt(6))/4. However, I then wondered what the result would be utilizing the half-angle formula. Using this, I found the answer to be (-2sqrt(2-sqrt(3))/4. I then set these answers equal to each other and found that -2sqrt(2-sqrt(3)) = sqrt(2) - sqrt(6). Therefore, is there a formula involving nested radicals (like the one found in the half-angle result) that says, for example, what sqrt(A - sqrt(B)) is equivalent to? I am unsure of the correlation between the two numbers on either side of the equation, so any starter help is greatly appreciated.
Thank you!
Currently, we are covering the trigonometric identities (half-angle, sum, difference, etc.). One particular problem asked to solve for the sin(195deg). So, I first attempted with the sum formula, splitting the 195 into 150 and 45. This yielded the result (sqrt(2) - sqrt(6))/4. However, I then wondered what the result would be utilizing the half-angle formula. Using this, I found the answer to be (-2sqrt(2-sqrt(3))/4. I then set these answers equal to each other and found that -2sqrt(2-sqrt(3)) = sqrt(2) - sqrt(6). Therefore, is there a formula involving nested radicals (like the one found in the half-angle result) that says, for example, what sqrt(A - sqrt(B)) is equivalent to? I am unsure of the correlation between the two numbers on either side of the equation, so any starter help is greatly appreciated.
Thank you!