Explain how the domain, range, maximum values, and minimum values compare between the sine and cosine functions and their reciprocals.

Write a diary entry from the perspective of a character in "Separating" other than Richard—either Joan or one of the children.

If the hypothesis is tested at the 5 % level of significance instead of 1 %, how will this affect the power of the test?

Write a paragraph explaining why the writing in Edgar Allan Poe's ''The Raven'' was effective at emphasizing Poe's ideas and achieving the Gothic mood he was aiming for.

Use the given figure to answer the following.

Which of the following lists shows the segments lengths in order from least to greatest?

(A) CD, AB, DE, BC, EF

(B) EF, DE, AB, BC, CD

(C) BC, DE, EF, AB, CD

(D) EF, BC, DE, AB, CD

Use an indirect proof to prove the Hinge Theorem.

Given:

$$\begin{aligned} &A B=D E\\ & A C=D F \\ & m \angle A>m \angle D \end{aligned}$$

Prove: BC>EF

Negating the conclusion, BC>EF, means that either BC is equal to EF, or BC is less than EF. Therefore, this theorem must be proven for both cases.

Case 1: BC=EF

Case 2: BC<EF

a. Write the indirect proof for Case 1, BC=EF.

b. Write the indirect proof for Case 2, BC<EF.

Which of the following is not an advantage of simulation?

a) Simulation is relatively straightforward and flexible.

b) Good simulation models are usually inexpensive to develop.

c) "Time compression" is possible.

d) Simulation can study the interactive effects of individual variables.

e) Simulations do not interfere with real-world systems.

in period 5 which has the largest atoms;

Why does it make sense that a graphing calculator has a sine regression option but not a cosine regression option?

Hannah is graphing the functions f(x)=5 $\sin (x)$ and g(x)=5 $\csc (x)$ on the same coordinate plane. State what she should see if she graphs them correctly.

For the trigonometric function, determine the vertical stretch or compression and the horizontal stretch or compression. Then, plot the function and ifnd its period.

$$y=\frac{1}{3} \sin 2 x$$

Determine the new function after the given transformation.

$$q(x)=-0.5(x+2)^2-12$$

6 units down

Do transformed functions of the form $f(x)=a \tan \left(\frac{1}{b} x\right)$ have the same behavior seen in the parent function, that is, f(-x)=-f(x) ? Justify your answer and how it helps to graph transformed functions.

Graph one cycle of the transformed tangent function g(x) together with the parent function f(x)=tan x. g(x)=-$\frac{1}{4} \tan 4 x$