Liceo De Pulilan Colleges
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Liceo De Pulilan Colleges Longos, Pulilan, Bulacan College Department PRELIMINARY EXAMINATIONS 2ND Semester S. Y. 2009 – 2010 Subject Code: Instructor: John Vincent G. Fajardo For: BSIT 1st yr
Subject Description: Trigonometry Date: Dec. 3 – 4, 2009
I.
Express each of the following in radian measure: 1. 25° 2. 18.34° 3. 75°30’ 4. 112°40’ 5. 12°12’20”
I.
Express each of the following in degree measure: 1. π4 rad 2. 7π10 rad 3. 5π6 rad 4. 14 rad 5. 75 rad
I.
Solve the following worded problems: 1. The minute hand of a clock is 12 cm long. How far does the tip of the hand move during 20 min? 2. A central angle of a circle of radius 30 cm intercepts an arc of 6 cm. Express the central angle θ in radians and in degrees. 3. A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 120 m? 4. A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min? 5. Assuming the earth to be a sphere of radius 3960 mi, find the distance of a point 36°N latitude from the equator. 6. Two cities 270 mi apart lie on the same meridian. Find their difference in latitude. Hint: radius of the earth is 3960 mi. 7. A sector of a circle has a central angle of 50_ and an area of 605 cm2. Find the radius of the circle. Hint: K=12r2θ;therefore r=2Kθ. 8. A sector of a circle has a central angle of 80° and a radius of 5 m. What is the area of the sector? 9. A wheel is turning at the rate of 48 r/min. Express this angular speed in (a) r/s, (b) rad/min, and (c) rad/s. 10. A wheel 4 ft in diameter is rotating at 80 r/min. Find the distance (in ft) traveled by a point on the rim in 1 s, that is, the linear velocity of the point (in ft/s).
Liceo De Pulilan Colleges Longos, Pulilan, Bulacan College Department PRELIMINARY EXAMINATIONS 2ND Semester S. Y. 2009 – 2010
Subject Code: Instructor: John Vincent G. Fajardo For: BSIT 1st yr
Subject Description: Trigonometry Date: Dec. 3 – 4, 2009
Answer Key: I. Express each of the following in radian measure: 1. 5π/36 or 0.4363 rad 2. 0.3201 rad 3. 151π/360 or 1.3177 rad 4. 169π/270 or 1.9664 rad 5. 0.2130 rad I.
I.
Express each of the following in degree measure: 1. 45° 2. 126° 3. 150° 4. 14°19’12” or 14.32° 5. 80°12’26” or 80.21° Solve the following worded problems: 1. 25.1 cm 2. 11.46° 3. 275 m 4. 0.2816 rad or 16.13° 5. 2488 miles 6. 3°54.4’ 7. 37.2 cm 8. 17.5 m2 9. (a) 4/5 r/s, (b) 301.6 rad/min, (c) 5.03 rad/s 10. 8π/3 rad/s
Subject Description: Trigonometry Date: Dec. 3 – 4, 2009
I.
Express each of the following in radian measure: 1. 25° 2. 18.34° 3. 75°30’ 4. 112°40’ 5. 12°12’20”
I.
Express each of the following in degree measure: 1. π4 rad 2. 7π10 rad 3. 5π6 rad 4. 14 rad 5. 75 rad
I.
Solve the following worded problems: 1. The minute hand of a clock is 12 cm long. How far does the tip of the hand move during 20 min? 2. A central angle of a circle of radius 30 cm intercepts an arc of 6 cm. Express the central angle θ in radians and in degrees. 3. A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 120 m? 4. A train is moving at the rate of 8 mi/h along a piece of circular track of radius 2500 ft. Through what angle does it turn in 1 min? 5. Assuming the earth to be a sphere of radius 3960 mi, find the distance of a point 36°N latitude from the equator. 6. Two cities 270 mi apart lie on the same meridian. Find their difference in latitude. Hint: radius of the earth is 3960 mi. 7. A sector of a circle has a central angle of 50_ and an area of 605 cm2. Find the radius of the circle. Hint: K=12r2θ;therefore r=2Kθ. 8. A sector of a circle has a central angle of 80° and a radius of 5 m. What is the area of the sector? 9. A wheel is turning at the rate of 48 r/min. Express this angular speed in (a) r/s, (b) rad/min, and (c) rad/s. 10. A wheel 4 ft in diameter is rotating at 80 r/min. Find the distance (in ft) traveled by a point on the rim in 1 s, that is, the linear velocity of the point (in ft/s).
Liceo De Pulilan Colleges Longos, Pulilan, Bulacan College Department PRELIMINARY EXAMINATIONS 2ND Semester S. Y. 2009 – 2010
Subject Code: Instructor: John Vincent G. Fajardo For: BSIT 1st yr
Subject Description: Trigonometry Date: Dec. 3 – 4, 2009
Answer Key: I. Express each of the following in radian measure: 1. 5π/36 or 0.4363 rad 2. 0.3201 rad 3. 151π/360 or 1.3177 rad 4. 169π/270 or 1.9664 rad 5. 0.2130 rad I.
I.
Express each of the following in degree measure: 1. 45° 2. 126° 3. 150° 4. 14°19’12” or 14.32° 5. 80°12’26” or 80.21° Solve the following worded problems: 1. 25.1 cm 2. 11.46° 3. 275 m 4. 0.2816 rad or 16.13° 5. 2488 miles 6. 3°54.4’ 7. 37.2 cm 8. 17.5 m2 9. (a) 4/5 r/s, (b) 301.6 rad/min, (c) 5.03 rad/s 10. 8π/3 rad/s
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