2015年8月6日 · The half angle identity for cosine can be derived (since I don't recall it off-hand): cos^2(x) = (1+cos(2x))/2 By inference: cos^2(x/2) = (1+cosx)/2 Square root to ...

Thus, the exact value of cos 22.5 degrees is 0.92387953. Here's the detailed solution.

2018年8月10日 · #cos (theta/2) = +- sqrt((1-cos theta) / 2)# Let #hat (theta/2) = 22.5^@#. #hat theta = 2 * 22.5 = 45 ^@# cos (theta/2) = cos 22.5^@ = + sqrt((1 - cos 45) / 2)#

2015年10月23日 · Since #22.5^@ = 1/2xx45^@# we will want to use the half angle formula for #cos#. #cos(theta/2) = +-sqrt((1+cos(theta))/2)#

2015年8月27日 · How do you find the exact value for #cos165# using the half‐angle identity?

For cos 22 degrees, the angle 22° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 22° value = 0.9271838. . . Since the cosine function is a periodic function, we can represent cos 22° as, cos 22 degrees = cos(22° + n × 360°), n ∈ Z. ⇒ cos 22° = cos 382° = cos 742°, and ...

2015年9月24日 · We have that. #cos(2a)=cos^2a-sin^2a=cos^2(a)-(1-cos^2a)=> cos^2(a)=1/2*(1+cos2a)=> cos(a)=1/sqrt2*sqrt(1+cos2a)#

2015年7月19日 · Find cos (22.5 deg) Call cos 22.5 = cos t --> cos 2t = cos 45 deg Trig table --> cos 45 = (sqrt2)/2 Use trig identity: cos 2t = sqrt2/2 = 2cos^2 t - 1 2cos^2 t = 1 + sqrt2/2 = (2 + sqrt2)/2 cos^2 t = (2 + sqrt2)/4 cos t = cos 22.5 = +- sqrt(2 + sqrt2)/2

2018年6月21日 · cos (22.5) = sqrt(2 + sqrt2)/2 cos (-22.5) = cos (22.5) Use half angle identity: cos (x/2) = +- sqrt((1 + cos x)/2) In this case, x/2 = 22.5, and x = 45 --> cos x ...

How do you use the half angle identity to find exact value of cos 22.5? How do you simplify #sin(theta/2)# using the double angle identities? How do you simplify #cos(theta/2)# using the double angle identities?