Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate. When necessary, use a substitution to reduce it to a standard form.

$$\int _ { - 1 } ^ { 1 } \sqrt { 1 + x ^ { 2 } } \sin x\ d x$$

Solve for

$$\theta , 0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$

, or for x,

$$0 \leq x < 2 \pi$$

.

$$\sin \left( 3 \theta - 25 ^ { \circ } \right) = \frac { \sqrt { 3 } } { 2 }$$

Why is the weather in New York State consistently cooler in January than it is in July? (1) Earth is closer to the sun in July (2) Cloudy weather is more common in January (3) The Northern Hemisphere is tilted away from the sun in January. (4) Sunlight is reflected away from Earth by ice and snow during January

Match the trigonometric expression with its simplified form. (a) sec x, (b) -1 (c) cot x, (d) 1, (e) -tan x, (f) sin x. $\frac{\sin (-x)}{\cos (-x)}$

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for

$$0 \leq x \leq 2 \pi.$$

y = 5 sin x

Describe and correct the error in solving the equation.

$$\left.\begin{aligned} 5 c - 6 & = 4 - 3 c \\ 2 c - 6 & = 4 \\ 2 c & = 10 \\ c & = 5 \end{aligned} \right.$$

Solve the equation.

$$( 2 b + 29 ) ^ { 1 / 3 } = 3$$

Model and find the difference using algebra tiles. 1 - (-5)

We are replicating an experiment. How will each of the following changes affect the power of our test? Indicate whether it will increase, decrease, or remain the same, assuming that all other aspects of the situation remain unchanged.

We increase the number of subjects from 40 to 100.

Does a higher rate of saving lead to higher growth temporarily or indefinitely?

Use a graphing utility to graph the sales function over 1 year, where S is the sales (in thousands of units) of a seasonal product, and t is the time (in months), with t = 1 corresponding to January. Determine the months of maximum and minimum sales. $S=56.25+9.50 \sin \frac{\pi t}{6}$

Find the product. Write your answer using exponents. (0.5) • (0.5)²

An assumption inherent in capital budgeting is that all positive net cash flows are reinvested at the MARR from the time they are realized until: (a) The end of the shortest-lived project (b) The end of the longest-lived project (c) The end of the respective project that generated the cash flow (d) The average of the lives of the projects included in the bundle

Use complex numbers to find an invertible matrix $P$ and a diagonal matrix $D$ such that $A=PDP^{-1}$.

$$\begin{bmatrix}2i&&0&&0\\0&&1&&-i\\0&&0&&0\end{bmatrix}$$