Tutor profile: Jon S.

Given sin x = 0.4, solve for x.

As is often the case for trig problems, the only way to get the "x" out of the expression "sin x" is to take the "inverse operation" on both sides. Since the function is sine, we use the inverse sine function. Therefore: sin x = 0.4 sin⁻¹ (sin x) = sin⁻¹ 0.4 x = sin⁻¹ 0.4 (which is a value that can be determined by a calculator). This pattern works for a wide variety of problems in Trig (and Precalculus).

Oceanic crust is generally much younger than the crust that makes up the continents. Explain why.

Along mid-ocean ridges, new oceanic crust is continually forming. Meanwhile, the oldest oceanic crust sinks (or "subducts") deep into the Earth along oceanic trenches. These ongoing processes mean that all oceanic crust is much younger than continental crust, which does not experience these processes.

Find the zeros of f(x)= x³+3x²-x-3 graphically.

Using an online graphing utility such as Desmos.com, the given function is plotted and the x-intercepts of the function are found. These are the values of x such that f(x)=0 -- that is, the "zeros" of the function. In this case, the x-intercepts are at (-1,0), (1,0), and (-3,0). This also ends up telling us that this function can be factored as (x+1)(x-1)(x+3).