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Popular Trigonometry >

sin(x)cos(y)-cos(x)sin(y)>= 0

Solution

sin (x) cos (y) - cos (x) sin (y) \geq 0

Solution

False for all x \in R

Solution steps

sin (x) cos (y) - cos (x) sin (y) \geq 0

Use the following identity:

- cos (s) sin (t) + cos (t) sin (s) = sin (s - t)

sin (x - y) \geq 0

Range of

sin (x - y) :

False for all

y \in R

sin (x - y) \geq 0 and

False for all

y \in R :

False

Let

y = sin (x - y)

Combine the intervals

y \geq 0 and False for all y \in R

Merge Overlapping Intervals

y \geq 0 and False for all y \in R

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

y \geq 0

and

False for all

y \in R

False for all y \in R

False for all y \in R

No Solution for x \in R

False for all x \in R

Popular Examples

cos(θ)>0,tan(θ)>0

sqrt(3)cot(x)<-1

10<5sin(pi/6 (x-10))+6