Kindly answer both correctly and write answer sepeartely 14. 0/1 pointsI Previou
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Kindly answer both correctly and write answer sepeartely
14. 0/1 pointsI Previous Answers SwokPreCalc12 6.2.059. My Notes Find the solutions of the equation that are in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 5-5sin t = 5V3 cos t 11n Need Help? E-Read t.ITalktoaTutod p? Read it Submit AnswerSave Progress Practice Another Version 15. 0/1 points Previous Answers SwokPreCalc12 6.2.061 My Notes Find the solutions of the equation that are in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 3cos + 3 sin = 3 Need Help?Read It Talk to a TutorExplanation / Answer
14. We have 5-5sin t =(53)(cos t) or, 5(1-sin t)=(5 3)(cos t) or, (1-sin t)= (3)(cos t) or, (1-sint)=(3)(1-sin2t). On squaring both the sides, we get (1-sint)2=3(1-sin2t) = 3(1+sint)(1-sint) . Thus, either sin t = 1 or, -1 or, 1-sint = 3(1+sint). If sin t = 1, then t = sin-1 1 = /2. If sin t = -1, then t = sin-1 (-1) = -/2 or, 3/2. If 1-sin t = 3(1+sin t) , then 4sin t = -2 or, sint = -1/2 so that t = sin-1(-1/2) = = -/6 or, t = 11/6. Both /2 and 11/6 are in the interval [0,2). Hence , either t = /2 or t =3/2 or, t = 11/6.
15. We have 3 cos +3 sin = 3 or, 3(cos + sin ) = 3 or, cos + sin = 1 or, sin = -cos or, tan = -1 so that = tan-1(-1) = -/4 or, 3/4. Since 3/4 lies in the interval [0,2), hence = 3/4.
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