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1 Name: _____________________________ Math In Trades Unit 6 – Triangle Trigonometry REVIEW ҉ DMS DD (Converting between Decimal Degrees & Degrees, Minutes, Seconds) Examples: Convert from decimal degrees to the nearest second. 1) 47 3/8º 2) 36 ¾º 3) 73 3/5º 4) 16.11º 3) 57º36’ 4) 168º54’ Examples: Round to the nearest thousandth of a degree 1) 1º12’ 2) 96º9’ ↔ Converting Between Degrees & Radians π radians = 180 degrees Examples: Convert all angle measures to radians. Round to three significant digits. 1) 10º45’ 2) 35.26º 3) 90º Examples: Convert to degrees and round to the nearest hundredth. 1) 0.05 rad 2) 4.3 rad 3) 1.43 rad 2 ∆ SOH CAH TOA sinA = opposite hypotenuse cosA = adjacent hypotenuse tanA = opposite adjacent Examples: Find the missing part of the triangle. 1) 2) 3) 4) 5) Find m <U 6) Find m <K 3 ↖→↙↓ Linear & Angular Speed (a = angle in radians) Linear Speed: v = d t Angular Speed: w = a t Examples: 1. If a car travels 1800 ft in 24 seconds, what is its average linear speed for the trip? 2. If a 24-in.-diameter flywheel rotates through an angle of 140º in 1.1 seconds, what is the average angular speed of the flywheel? 3. A belt-driven drum of radius 28.4 cm makes one revolution every 0.250 sec. What is the linear speed of the belt driving the drum? Round to three significant digits. (Hint: If the belt doesn’t slip, the distance traveled by the belt in one revolution is equal to the circumference of the drum) 4. The blade on a shop fan rotates at 8.0 rev/sec. Calculate its average angular speed. Round to two significant digits. (Hint: each revolution is 360º) 4 ⃝ Sectors (REMEMBER: a = angle IN RADIANS) Examples: 1. A sheet metal worker wants to know the arc length and area of a sector with central angle 150º cut from a circular sheet of metal with radius 16.0 in. 2. Calculate the arc length and area of a sector with central angle 80º and radius 25.0 ft. Round to three significant digits.