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What are all the options for x in 2tanx=3sinx?

Answer 1

Violet Anderson

#x= 0+pin#
#x=0.841 +2pin#
#x=-0.841 +2pin#

#n# is an element of all integers

#2tanx=3sinx#

#2tanx-3sinx=0#

#sinx(2secx-3)=0#

#sinx=0# #x= 0, pi# #x= 0+pin#

#secx=3/2#

Reciprocate both sides: #cosx=2/3#

#x= arccos(2/3)=0.841 +2pin#

In quadrant four, Arccosine omits a potential solution, which can be discovered by (HINT: DRAW A TRIANGLE IN THE FOURTH TRIANGLE AND SOLVE FOR THE OPPOSITE LEG):

#x= arcsin(-sqrt5/3)= -0.841 +2pin#

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Answer 2

Adam Aguirre

To find all the options for ( x ) in the equation ( 2\tan(x) = 3\sin(x) ), we need to solve the equation. After solving it, we will obtain the values of ( x ) that satisfy the equation.

[ 2\tan(x) = 3\sin(x) ]

[ \frac{2\tan(x)}{\sin(x)} = 3 ]

[ \frac{2\sin(x)/\cos(x)}{\sin(x)} = 3 ]

[ \frac{2}{\cos(x)} = 3 ]

[ 2 = 3\cos(x) ]

[ \frac{2}{3} = \cos(x) ]

[ x = \arccos\left(\frac{2}{3}\right) ]

The solutions for ( x ) in the given equation are ( x = \arccos\left(\frac{2}{3}\right) ) and any other angles that are coterminal with ( x ).

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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.