7.4.3 – applications of trig equations. trig equations may be used to model situations where...
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7.4.3 – Applications of Trig Equations
• Trig equations may be used to model situations where things are cyclical, or repeating• Any examples you can think of from nature?
• Using trig equations, we can solve for particular information such as;• Dates of certain hours of sunlight• Tidal movements• Temperatures • Position of objects on circular motions or similar
Applied vs. Non-Applied Solutions
• In most real life cases, we will talk in terms of degrees when referring to the solutions for the equations • But, the variable may represent something other than angles; could
represent time, months, etc.
• Example. When an object is shot in the air according to the angle θ, we can determine the range of the object traveled by the equation:
• r = (1/32) v20 sin(2θ)
• V0 = initial velocity
• If a rock is shot in the air with an initial velocity of 400 feet per second and the rock lands 700 feet from where it was launched, determine the angle θ from the range using the previous equation.
• Example. The number of hours of sunlight per day for Atlanta, GA may be modeled by;• h = 2.325 sin(pi/6) (t – 2.667) + 12.155, where t is measured in
months and t = 0 represents January 1st.
• During which days, approximately, are there 13 hours of sunlight?
• Example. The tide, or depth of the ocean near the shore, changes throughout the day due to the revolution of the moon about Earth. The depth of a particular bay may be modeled as; • d = 25 – 28 cos((t)pi/6.2)• d will represent the water depth in feet and t is the time in hours; t =
0 will represent 12:00am. When do the high and low tides occur?
• Assignment. Research online to find two other potential applications of trig equations. You must bring your two applications and two equations to share. These may be ANY applications, including those we just mentioned (you just cannot use the same problem). To help search, look for topics like;
• Applications of trig graphs• Applications of trig functions• Trig equations in real life• Examples of trig equations and applications• Trig and science