MA 154 Exam 1 Summer 2005

Place your answers in the spaces provided. You must show correct work to receive credit.

(6 pts.) 1. Find the angle that is supplementary to the angle 36° 14' 55". Round your answer to the nearest second.

(8 pts.) 2. Find the area of the sector of a circle that is created by a central angle of 50º subtending a circular arc of length of 2.5 cm. Round your answer to the nearest tenth of a cm2.

(6 pts.) 3. Approximate to four decimal places.


(12 pts.) 3. a) Find the exact value of for the acute angle q if .

Please draw a triangle in the correct quadrant to represent θ.

b) Find the exact value of if and .

Please draw a triangle in the correct quadrant to represent θ.

(8 pts.) 5. Find the exact value:

a)

b)


(10 pts.) 6. One end of a guy wire is attached to the top of a 50 foot tower and the other end

is attached to the level ground such that it makes a angle with the

ground. To the nearest tenth of a foot, how long is the guy wire? Draw and label a picture representing the problem, setup an equation and solve.

(6 pts.) 7. Verify the identity by transforming the left side into the right side. Do not skip any steps. Including an extra step is better than excluding a necessary one.


(8 pts.) 8. Find the exact value of if q is in standard position and the terminal side of q goes through the point . Please draw a triangle in the correct quadrant to represent θ.

(6 pts.) 9. The following expression is equivalent to which of the following? Circle the correct answer. Your work will not be graded, only the answer. Guessing is allowed and will receive full credit, if correct. Treat this like an identity.

= ?

A.

B.

C.

D.

E. None of the above.


(6 pts.) 10. Find the amplitude, period and phase shift of the equation.

Amplitude
Period
Phase Shift

(12 pts.) 11. Approximate, to the nearest 0.01 radians, all angles q in the interval [0, 2p) that satisfy the equation:

a)

b)

(12 pts.) 12. Find the amplitude, period, phase shift, a, b, c, and equation, in the form , where a > 0, b > 0 and c is the least positive value, of the equation graphed below. Show your work.

Amplitude: / Period: / Phase
Shift:
a: / b: / c:
Equation:

1