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Find the solutio of 4sin 4theta+1=root5?

Answer 1

Madelyn Adams

#theta# = #(npi)/2# +#pi/40#
#theta# = #(npi)/2#+#(9pi)/40#

for # n in ZZ#

Rearanging; #sin4theta = (5^(1/2) -1)/4# #sin4theta = sin(arcsin( (5^(1/2) -1)/4 )) # #sin4theta = sin(pi/10)#

Now we can consider the general solution to sin#x# = #sina#

The solution to this is #x# = #2npi + a# and #x# = #2npi + pi - a# for all integers n

so hence #4theta = 2npi + pi/10 and 4theta = 2npi + (9pi)/10 #

Hence dividing by 4, yields;

#theta# = #(npi)/2# +#pi/40# #theta# = #(npi)/2#+#(9pi)/40#

for # n in ZZ#

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Answer 2

Victoria Adebayo

To find the solution of (4\sin(4\theta) + 1 = \sqrt{5}), first, subtract 1 from both sides, then divide by 4. After that, take the inverse sine (arcsin) of both sides. Finally, divide by 4 again to solve for (\theta).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.