Question : A river is 600 m wide. A boat enters the water and is pushed by the current at an angle of 30° to its : 2163396

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) Suppose (π/4) ≤ x ≤ (3π/4). Which of the following statements can be made abouttanx?

A) tanx is positive.

B) tanx is not defined.

C) Iftanx is defined, then |tanx| ≥ 1.

D) tanx is defined.

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

2) Give the values of tant and sect, where t is the radian measure of the angle shown.

Enter just a, b where a represents tant and b representssect. (no labels and no approximations).

3) Give the values of tant and sect, where t is the radian measure of the angle shown.

Enter just a, b where a represents tant and b representssect with any fractions reduced of form (c/D) (no labels and no approximations).

4) Give the values of tant and sect where t is the radian measure of the angle shown.

Enter just a, b where a represents tant and b representssect, fractions and quotients reduced of form (c/D) or (√(f)/g) (no labels and no approximations).

5) A river is 600 m wide. A boat enters the water and is pushed by the current at an angle of 30° to its original position. How far downstream from its original position will the boat land?

Enter your answer in the reduced form a√(B) (no units).

6) A ladder leaning against a building makes an angle of 60° with the ground. If the base of the ladder is 3 feet from the building, how far up the building will the ladder reach? Enter your answer in the reduced form a√(B) (no units).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the indicated trigonometric function, where θ is the radian measure of the given angle. Give an exact answer with a rational denominator.

7) Find secθ.

A) (5√(106)/106)

B) (√(106)/5)

C) (9√(106)/106)

D) (5√(106)/9)

8) Findtanθ.

A) (√(58)/3)

B) (√(58)/7)

C) (7/3)

D) (3/7)

Find the derivative of the function.

9) y = cot(5x - 3)

A) (dy/dx) = - csc²(5x - 3)

B) (dy/dx) = 5cot(5x - 3)csc(5x - 3)

C) (dy/dx) = -5csc²(5x - 3)

D) (dy/dx) = -5sec²(5x - 3)

10) y = x⁷ - cscx + 17

A) (dy/dx) = 7x⁶ + cscxcotx

B) (dy/dx) = 7x⁶ + cot²x

C) (dy/dx) = x⁶ - cot²x + 17

D) (dy/dx) = 7x⁶ - cscxcotx

Differentiate.

11) f(x) = e^3x tan(x²)

A) 3e^xsec²x²

B) 3e^3xtanx² + 2xe^3xsec²(x²)

C) 6xe^xsec²x²

D) 3e^xtanx² + e^3xsec²x²

E) none of these

12) f(x) = (sinx + cosx)⁵

A) 5(sinx + cosx)⁴(cosx - sinx)

B) 5(sinx + cosx)⁵

C) (cosx - sinx)⁵

D) 5(sinx + cosx)⁴

E) none of these

13) f(x) = tan(cosx)

A) tan(- sinx)

B) sec²(cosx)

C) - sinxsec²(cosx)

D) tan(cosx)sec(cosx)

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

14) f(t) = ln(sect)

Do not label your answer, no parentheses.

15) f(x) = 2secx

Enter your answer without parentheses, secants before tangents in terms, no labels.

16) f(x) = 2cot³x

Enter your answer without parentheses, no labels, use the multiplication dot between functions..

17) f(x) = tan(3x)sinx

Enter your answer without parentheses, no labels, any term containing sine appearing first.

18) f(x) = √(tanx + sinx)

Enter your answer without parentheses, no labels. Enter a quotient (a/b√(C) ).

19) f(x) = e^{x^3}⋅tan2x

Enter your answer without parentheses except as indicated in this form, e^P(x)(ab + 2D) .

20) f(x) = ln(e^x⋅tan2x)

Enter your answer without parentheses or labels, no multiplication dot.