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Solve for (0<x<360) tan2x=-1 ?

Asher Friedman · Accepted Answer

#x= 67.5', 112.5', 247.5', 292.5'# #tan2x=-1# Currently, the range is #0 < x < 360# Now, since you have #tan2x# where it is #2x# and not #x#, we can change the range to: #0 < 2x < 720# #tan2x=-1# Now remember that #tan2x# is negative in the second and fourth quadrant. Also recall that #tan45=1# so for the negative version of 1, you either add or subtract 45 from the second and fourth quadrant. #2x= 180-45, 180+45, 540-45, 540+45# #2x= 135, 225, 495, 585# Divide each angle by 2 because you want it equal to #x# and not #2x# #x= 67.5, 112.5, 247.5, 292.5#

Dylan Arnold · Answer

# 67.5^circ, 157.5^circ, 247.5^circ, 337.5^circ# #tan 2x = -1# #2x = 135^circ + 180^circ k quad# integer #k# #x= 67.5^circ +90^circ k #

Madelyn Adams · Answer

# x=(67.5)^circ , (157.5)^circ , (247.5)^circ , (337.5)^circ#

Here,

#tan2x=-1 ,where , 0 < x <360^circ#

#=>tan2x=tan(-pi/4) ,where , 0< x < 2pi#

So,

#2x=kpi-pi/4 ,kin ZZ#

#color(red)(=>x=kpi/2-pi/8 , kin ZZ#

Take,

#k=0=>x=-pi/8 !in(0,2pi)#

#color(blue)(k=1=>x=pi/2-pi/8=(3pi)/8 in (0,2pi)#

#color(blue)(k=2=>x=pi-pi/8=(7pi)/8 in (0,2pi)#

#color(blue)(k=3=>x=(3pi)/2-pi/8=(11pi)/8 in (0,2pi)#

#color(blue)(k=4=>x=2pi-pi/8=(15pi)/8 in (0,2pi)#

#k=5=>x=(5pi)/2-pi/8=(19pi)/8 !in (0,2pi)#

Hence,

#x=(3pi)/8 , (7pi)/8 , (11pi)/8,(15pi)/8.#

#i.e. x=(67.5)^circ , (157.5)^circ , (247.5)^circ , (337.5)^circ#

Carter Anderson · Answer

undefined To solve the equation tan(2x) = -1 for the given domain 0 < x < 360, you can follow these steps:

1. First, find the solutions for 2x by using the inverse tangent function: arctan(-1) = -π/4 or 3π/4.

2. Then, solve for x by dividing each solution by 2: 
   -π/4 ÷ 2 = -π/8 or 3π/8
   3π/4 ÷ 2 = 3π/8

3. Since the domain is restricted to 0 < x < 360, you need to consider the solutions within this range:
   -π/8 + 360n, where n is any integer.
   3π/8 + 360n, where n is any integer.

Therefore, the solutions for the equation tan(2x) = -1 within the given domain are:
x = 67.5° + 180°n or x = 202.5° + 180°n, where n is any integer.

Solve for (0&lt;x&lt;360) tan2x=-1 ?

Solve for (0<x<360) tan2x=-1 ?