Arkansas Tech UniversityMATH 1203: Trigonometry

Dr. Marcel B. Finan

Review Problems for Test #2

Exercise 1Find the measure in radians of a central angle θ of a circle of radius r = 5.2 cmsubtended by the arc s = 12.4 cm.

Exercise 2Find the measure of the reference angle θ′ corresponding to the angle θ =−475◦.

Exercise 3Use the trigonometric identities to write the expression

1

1− sin t+

1

1 + sin t

in terms of a single trigonometric function.

Exercise 4Find the value of sin θ given that sec θ = 2

√3

3and 3π

2< θ < 2π.

Exercise 5Convert 3.402◦ to DMS measure.

Exercise 6A car with wheel of radius 14 inches is moving with a linear speed of 55 mph.Find the angular speed ω of the wheel in radians per second. Recall that1 mile = 63483 in.

Exercise 7Let θ be an acute angle of a right triangle and sin θ = 3

5. Find tan θ.

Exercise 8Find the values of the six trigonometric functions of θ for the right triangle

1

with the given sides.

Exercise 9Use an reference angle, to evaluate csc 4π

3. DON’T use a calculator!

Exercise 10Find the value of the six trigonometric functions for the angle whose terminalside passes through the point P (2, 3).

Exercise 11Factor: 2 sin2 t− sin t− 1.

Exercise 12Find the measure of the complement and the supplement of the angle 56◦33′15”

Exercise 13Find the measure of the intercepted arc of a circle of radius r = 8 inchesand central angle θ = π

4.

Exercise 14Let θ be an acute angle of a right triangle and tan θ = 4

3. Find cot θ and

sec θ.

Exercise 15Find (without a calculator) the exact value of the expression: sin π

3cos π

4−

tan π4.

Exercise 16Let θ be an angle in standard position such that cos θ > 0 and tan θ < 0.State the quadrant in which the terminal side of θ lies.

Exercise 17Use reference angles in finding the exact value of cot 540◦.

2

Exercise 18Find the wrapping functionW (t) when t = 7π

6. Recall thatW (t) = (cos t, sin t).

Exercise 19Write csc t in terms of cot t, π

2< t < π.

Exercise 20Graph one full cycle of the function f(x) = 2 cos (πx).

Exercise 21Sketch one full period of y = 4 sin 2πx

3

Exercise 22sketch one full period of y = 3 tan 2πx

Exercise 23Sketch one full period of y = −2 secπx

Exercise 24Graph one full cycle of the function f(x) = 3 csc

(π2x).

Exercise 25Graph f(x) = 3 tan πx for −2 ≤ x ≤ 2.

3