Find tan (22.5)
Answer: #-1 + sqrt2#
Explanation:
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 = tan (22.5) = - 1 +- sqrt2#
Since tan 22.5 is positive, then take the positive answer:
tan (22.5) = - 1 + sqrt2
A. 4 2/3
B. 3 1/2
C. 3 2/3
D. 4 3/4
E. 3
F. 4 5/6
Answer:
Pretty sure it's B
Step-by-step explanation:
Everything else would be more like an equation. I think B is the only inequality.
Answer:
He is not correct, the answer is All Real Numbers.
Step-by-step explanation:
When two lines are right on top of each other, the solution set is All Real Numbers that are on both lines because the solution set is the point(s) at which the lines overlap.
