A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).
A relation in mathematics that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality. When comparing two numbers on a number line, it is most frequently used to compare their sizes.
5 sin(x) > 5 cos(x)
To removing constant we divide both the side by 5:
5sin(x) > 5 cos(x)
sin(x) > cos(x)
sin x > cos x;
sin x = cos x; tan x = 1; x = π/4 or x = 5π/4
sin x > cos x for x ∈ (π/4, 5π/4)
A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).
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Find all values of x in the interval [0, 2] that satisfy the inequality. (Enter your answer using interval notation.) 5 sin(x) > 5 cos(x)