Jul 19, 2015 · Find tan (22.5) Answer: -1 + sqrt2 Call tan (22.5) = tan t --> tan 2t = tan 45 = 1 Use trig identity: tan 2t = (2tan t)/(1 - tan^2 t) (1) tan 2t = 1 = (2tan t)/(1 - tan^2 t) --> --> tan^2 t + 2(tan t) - 1 = 0 Solve this quadratic equation for tan t. D = d^2 = b^2 - 4ac = 4 + 4 = 8 --> d = +- 2sqrt2 There are 2 real roots: tan t = -b/2a +- d/2a = -2/1 + 2sqrt2/2 = - 1 +- sqrt2 Answer: tan t ...

Nov 16, 2016 · How do you use the half angle identify to find the exact value of #tan22.5^circ#?

Half angle Identities in term of t = tan a/2. 2. #sin a = (2t)/(1 + t^2)# 3. #cos a = (1 - t^2)/(1 + t^2)#

Mar 26, 2018 · To figure out the #tan# of #22.5^@#, use the #tan# half-angle formula. I personally like the second one the best, so I'll use that one: I personally like the second one the best, so I'll use that one:

Jul 14, 2015 · Using the half angle formula you get: #sin^2(theta)=1/2[1-cos(2theta)]# if #theta=22.5°# then #2theta=45°# so you get:

Aug 6, 2015 · 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 ...

Jul 22, 2015 · Call tan 112.5 = tan t tan 2t = tan 225 = tan (45 + 180) = tan 45 = 1 Use trig identity: #tan 2t = (2t)/(1 - t^2)#-->

Feb 11, 2017 · How do you use the half angle formulas to determine the exact values of sine, cosine, and tangent of the angle #112^circ 30'#?

Jul 30, 2015 · Find tan (67.5) deg Ans: 1 + sqrt2 Call tan (67.5) = t . tan 2t = tan (135) = tan (-45 + 180) = - tan (45) = - 1 Use trig identity: tan 2t = -1 = (2t)/(1 - t^2) t^2 - 2t - 1 = 0 D = d^2 = b^2 - 4ac = 4 + 4 = 8 --> d +- 2sqrt2 t = tan (67.5) = 1 +- sqrt2 Since the arc (67.5) is in Quadrant I, only the positive number is accepted -> tan (67.5) = 1 + sqrt2

Aug 2, 2015 · Simplify tan ((9pi)/8) tan ((9pi)/8) = tan (pi/8 + pi) = tan pi/8 Call tan pi/8 = t tan 2t = tan ((2pi)/8) = tan (pi/4) = 1 Use trig identity: tan 2t = 2t/(1 - t^2 ...