True of False? In Exercises 51–54, determine whetherthe statement is true or false. Justify your answer.51. Because sin(−t) = −sin t, the sine of a negative angleis a negative number.52. The real number 0 corresponds to the point (0, 1) on theunit circle.53. tan a = tan(a − 6π)54. cos(−7π2 ) = cos(π +π2)

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A: Given query is to find statement is true or false.

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A: Okay I am solving first question as you mentioned.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.