ANALYTICAL METHOD OF VECTOR ADDITIONVectorsCP-02Page 24Rev. 0Figure 23 Trigonometric FunctionsFigure 24 Hypotenuse and AngleAlso, recall the three trigonometric functionsreviewed in an earlier chapter and shown inFigure 23. The cosine will be used to solve forF . The sine will be used to solve for F .x yTangent will normally be used to solve for ,although sine and cosine may also be used.On a rectangular coordinate system, the sinevalues of are positive (+) in quadrants I and IIand negative (-) in quadrants III and IV. Thecosine values of are positive (+) in quadrantsI and IV and negative (-) in quadrants II and III.Tangent values are positive (+) in quadrants Iand III and negative (-) in quadrants II and IV.When mathematically solving for tan , calculators will specify angles in quadrants I and IV only.Actual angles may be in quadrants II and III. Each problem should be analyzed graphically toreport a realistic solution. Quadrant II and III angles may be obtained by adding or subtracting180 from the value calculated.oUsingtheAnalyticalMethodTo illustrate this method, consider this example: a man walks 3 miles in one direction, then turns90 and continues to walk for an additional 4 miles. In what direction and how far is he from hisostarting point? The first step in solving this problem is to draw a simple sketch as shown in Figure24.

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