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P.o.D. โ Solve each triangle using the Law of Cosines/Sines. 1.) a=7, b=4, C=102 degrees. Find c. 2.) C=59 degrees, a=13, b=12. Find c. 3.) a=13, b=6, c=15. Find A. 4.) a=7, b=7, C=85 degrees. Find c. 5.) a=18, b=24.5, C=20 degrees. Find c. 10-9: Radian Measure Learning Target(s): I can approximate values of trigonometric functions using a calculator; convert angle measures from radians to degrees or vice versa. Angles have two sides: 1. 2. An _____________ side A ______________ side Terminal Side Initial Side - The _____________ of the two __________ is known as the ____________. - An angle centered at the ____________ is said to be in ________________ Position. - ___________ angles are measured ____________________________. - ___________ angles are measured ____________________. - If two angles have the same _____________, then they are said to be ______________________. Radian vs. Degree: - Just as distance may be measured in feet and centimeters, angles can be measured in both ____________ and ____________. Definition of a Radian: ๐ ๐ = , where s is the ________ length and r is the ______________. ๐ Conversion Factors: 2๐ ๐๐๐๐๐๐๐ = ๐ ๐๐๐๐๐๐๐ = 1 ๐๐๐๐๐๐ โ Some Other Common Radian Measures: 45° = ๐๐๐๐๐๐๐ 60° = ๐๐๐๐๐๐๐ 30° = ๐๐๐๐๐๐๐ 90° = ๐๐๐๐๐๐๐ Acute Angles are between 0 and Obtuse Angles are between EX: For the positive angle angle. 9๐ 4 and radians. radians. subtract 2๐ to obtain a coterminal EX: For the positive angle 5๐ 6 subtract 2๐ to obtain a coterminal angle. EX: For the negative angle โ 3๐ 4 , add 2๐ to find a coterminal angle. Recall your Quadrants for Geometry: In Q1 ๏ In Q2 ๏ In Q3 ๏ In Q4 ๏ Complementary โ two angles whose sum is degrees. radians or Supplementary โ two angles whose sum is radians or ๐ EX: Find the complement and supplement of . 6 EX: Find the complement and supplement of 5๐ 6 . degrees. *There are _____ degrees or radians in a circle. Conversions Between Degrees and Radians: 1. 2. To convert degrees to radians, multiply degrees by To convert radians to degrees, multiply radians by EX: Convert 60 degrees to radians in terms of pi. EX: Convert 320 degrees to radians in terms of pi. EX: Convert -30 degrees to radians in terms of pi. ๐ EX: Express as a degree measure. 6 EX: Express 5๐ 3 as a degree measure. EX: Express 3 radians as a degree measure. Recall: ๐ = ๐ ๐ Arc Length: . . ๐ = ____, where r is the ___________ and theta is the measure of the central ____________. - It is important to note that ______ must always be in ____________ when used in a formula. EX: A circle has a radius of 27 inches. Find the length of the arc intercepted by a central angle of 160 degrees. Linear Speed (v): Linear Speed v = Angular Speed ๐ (omega): ๐= ๐โ๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐๐ก๐๐๐ ๐๐๐๐๐ = ๐ก๐๐๐ EX: The second hand of a clock is 8 centimeters long. Find the linear speed of the tip of this second hand as it passes around the clock face. EX: The circular blade on a saw rotates at 2400 revolutions per minute. Find the angular speed in radians per second. EX: Referring to the previous problem, the blade has a radius of 4 inches. Find the linear speed of a blade tip in inches per second. Area of a Sector: ๐ด= EX: A sprinkler on a golf course is set to spray water over a distance of 75 feet and rotates through an angle of 135 degrees. Find the area of the fairway watered by the sprinkler. Do the following on your own: a.) b.) Convert 1 degree to radians. Convert 60 degrees to radians. c.) Convert 5๐ 6 radians to degrees. Use a calculator to evaluate each of the following in radian mode. a.) Cos(6) b.) tan 7๐ 6 HW Pg. 715 1-28 Quiz 10.5-10.9 tomorrow