how did expanded trade affect china's population during the postclassical era?

Answer:

[tex]\cos(150) = -\frac{\sqrt 3}{2}[/tex]

Explanation:

An example is as follows;

Using reference angle, evaluate [tex]\cos(150)[/tex]

Solution:

We have: [tex]\cos(150)[/tex]

150 degrees is in the second quadrant, and it makes 30 degrees (i.e. 180 - 150) with the x-axis.

This implies that, cos(150) has the same magnitude as cos(30);

The only difference in the values is the sign; because

So, we have:

[tex]\cos(150) = -\cos(30)[/tex]

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[tex]\cos(30) = \frac{\sqrt 3}{2}[/tex]

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[tex]\cos(150) = -\frac{\sqrt 3}{2}[/tex]

Answer:

Amplitude: [tex]A = 4[/tex]

Period: [tex]\tau = \pi[/tex]

Minimum: -4

Maximum: 4

Intercepts: [tex]x = \frac{1}{2}\cdot [0 \pm \pi \cdot n][/tex], [tex]\forall \,n\in \mathbb{N}_{O}[/tex]

Explanation:

The expression described on statement is a sinusoidal formula, whose expression is of the form:

[tex]y = A\cdot \sin \left(\frac{2\pi\cdot x}{\tau}\right)[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]A[/tex] - Amplitude.

[tex]\tau[/tex] - Period.

By direct comparison, we calculate the amplitude and period:

Amplitude

[tex]A = 4[/tex]

Period

[tex]\frac{2\pi}{\tau} = 2[/tex]

[tex]\tau = \pi[/tex]

Minimum and Maximum

The sine is a bounded function between -1 and 1, meaning that sinusoidal formula is bounded between [tex]-A[/tex] and [tex]A[/tex]. Hence, the minimum and maximum are -4 and 4, respectively.

Intercepts

The intercepts are set of points of the sinusoidal formula such that [tex]y = 0[/tex]. The sine function is a periodic function which equals 0 each [tex]\pi[/tex] radians.

[tex]4\cdot \sin 2x = 0[/tex]

[tex]\sin 2x = 0[/tex]

[tex]2\cdot x = \sin^{-1} 0[/tex]

[tex]x = \frac{1}{2}\cdot \sin^{-1} 0[/tex]

[tex]x = \frac{1}{2}\cdot [0 \pm \pi \cdot n][/tex], [tex]\forall \,n\in \mathbb{N}_{O}[/tex]