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
7/5 - 10/5 = -3/5
I hope this helps.
Pat attention to the ending of the numbers. If there are an odd amount of odds, it's going to be odd. If there is an even amount of odds, it's going to be even. If there's only evens, it's only going to stay even.
Answer:
Step-by-step explanation:
Gabrielle and John each
wrote the prime factorization of 64.
64 can be break into 32 times 2
32 can be break into 16 times 2
16 can be break into 8 and 2
8 can be break into 4 times 2
4 can be break into 2 times 2
So 64 is equal to 2 times 2 times 2 times 2 times 2 times 2
