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Need help finding the second positive values for this trig equation? |
Hi, can someone help my find the second positive value, I got the first one from (inverse.cos.13/15)梅90, which is 0.33. The question is The height, h centimeters, of a bicycle pedal above the ground at time t seconds is given by the equation: h=30+15cos90t Find the first two positive values of t for which the height of the pedal is 43cm. Hi, In the equation h=30+15cos90t, the normal period for a cosine graph is changed from 360degrees to 360/90 or 4. So the cosine graph has to return to its highest position again at x = 4. This means the 2nd occurrence of a height of 43 cm will be before 4. The first occurrence of a height of 43 was correctly calculated to be at .33. It so happens that the next occurrence will be .33 before arriving back at the starting position when t = 4. That would be at 4 - .33 = 3.67. That's because cosine is positive in the 1st and 4th quadrants so these positive cosine values have to occur in the first and fourth parts of the period, namely between 0 and 1 and then between 3 and 4. A second way to get this, or to verify it is on a graphing calculator. Type in the equations: Y1 = 30 + 15cos(90x) Y2 = 43 Set your window to xmin=0, xmax=4, ymin=0, ymax=50, and yscl=10. Then graph. Use the [CALC] and intersect commands which will show you intersections at (.33251594,43) and (3.6674841,43). I hope that helps!! :-) err umm no sorry 43=30+15cos90t 15cox90t = 43 - 30 cos90t = 13/15 90t = 29.93, 360-29.93 90t = 29.93, 330.07 t = 0.333, 3.67 (to 3 significant figures) |
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