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Popular >

x=-4\land csc(x)>0

Solution

x = - 4 and csc (x) > 0

Solution

False for all x \in R

Solution steps

x = - 4 and csc (x) > 0

csc (x) > 0 :

False for all

x \in R

csc (x) > 0

Express with sin, cos

csc (x) > 0

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

\frac{1}{sin ( x )} > 0

\frac{1}{sin ( x )} > 0

If

\frac{1}{a} > 0

then

a > 0

sin (x) > 0

No Solution for x \in R

Combine the intervals

x = - 4 and False for all x \in R

Merge Overlapping Intervals

x = - 4 and False for all x \in R

The intersection of two intervals is the set of numbers which are in both intervals

x = - 4

and

False for all

x \in R

False for all x \in R

False for all x \in R

Popular Examples

cos(θ)<0\land (cos(θ))(sin(θ))<0

cos (θ) < 0 and (cos (θ)) (sin (θ)) < 0

cosh(θ)= 15/4 \land θ<0,sinh(θ)

cosh (θ) = \frac{15}{4} and θ < 0, sinh (θ)

2pi>sqrt(3)tan(θ)+1>= 0

2 π > 3 tan (θ) + 1 \geq 0

sin(3x)0<= x<= 2pi

sin (3 x) 0 \leq x \leq 2 π

sin(θ)=-0.616\land tan(θ)>0

sin (θ) = - 0.616 and tan (θ) > 0