$$\tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$$

Question 1

Which of the following is the correct formula for the sine of the sum of two angles $$A$$ and $$B$$?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

Question 2

If $$	an 37^\circ = \frac{3}{4}$$, what is the value of $$	an 53^\circ$$?

Accepted Answer

$$\frac{4}{3}$$

Question 3

Which of the following is the correct logarithmic identity for $$\log_a (mn)$$?

Accepted Answer

$$\log_a (mn) = \log_a m + \log_a n$$

Question 4

Given $$\cos(180^\circ - 	heta) = -\cos 	heta$$, what is $$\cos(180^\circ + 	heta)$$?

Accepted Answer

$$-\cos 	heta$$

Question 5

If $$\sin 37^\circ = \frac{3}{5}$$ and $$\sin 53^\circ = \frac{4}{5}$$, what is $$\cos 37^\circ$$?

Accepted Answer

$$\frac{4}{5}$$

Question 6

Which of the following is the correct formula for $$	an(A+B)$$?

Accepted Answer

$$	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$$

Question 7

A business's profit $$P is $$modeled by $$P(x) = 5x^2$ - 20x + 15. $$What is the value of $$x$$ that maximizes profit?

Accepted Answer

$$x = 2$$

Question 8

Which of the following is the correct formula for converting a natural logarithm to a common logarithm?

Accepted Answer

$$\log_{10} x = \frac{\ln x}{2.303}$$

Question 9

If $$\cos^2$ 	heta = 1 - \sin^2$ 	heta$$, what is $$\sin^2$ 	heta + \cos^2$ 	heta$$?

Accepted Answer

$$1$$

Question 10

A company’s revenue is given by $$R(x) = 100x - x^2$. What is the marginal revenue when x = 10$?

Accepted Answer

$$80$$

Question 11

Which of the following is the correct formula for $$\cos(A+B)$$?

Accepted Answer

$$\cos(A+B) = \cos A \cos B - \sin A \sin B$$

Question 12

If $$\log_a b = x$$, what is $$b in $$terms of $$a$$ and $$x$$?

Accepted Answer

$$b = a^x$$

Question 13

Which of the following is the correct formula for the derivative of $$y = e$$^{kx}$$ with respect to x$?

Accepted Answer

$$\frac{dy}{dx} = k e$$^{kx}$$

Question 14

If $$\sin(90^\circ - 	heta) = \cos 	heta$$, what is $$\cos(90^\circ - 	heta)$$?

Accepted Answer

$$\sin 	heta$$

Question 15

Which of the following is the correct formula for the slope of the tangent to the curve $$y = f(x) at$$ $$x = a$$?

Accepted Answer

$$\left. \frac{dy}{dx} \right|_{x=a}$$

Essential Trigonometric and Logarithmic Concepts for Business Calculus

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