please do the following problems and show the work

Derivatives of Trigonometric Functions Theorem 31 [Squeeze Theorem} Suppose that his] 5 x] E g[s'} for all. :r in: an interval containing a (steep: possibly at a itself}. If Elvis] = lirn 9(1) = L zIro. the-n. lirn HI] exists and is equal to L- zII-a. The Squeeze Theorem can be used to nd limits that might otherwise be difcult to calculate. In the following exercises. you will use the Squeeze Theorem to calculate some very important limits in trigonometry. 11?. {a} Draw a circle centered at the origin [3 with radius 1. Marl: the point where the circle crosses the saxis with the label A. {b} h'larl: a point on the circle in lQuandrant 1. Label this point C'- Use a straight edge to draw a ray from the origin through the point 1'3". Continue this ray going outward into IQuadrant 1. Label the angle formed between this ray and the :rasis as H. Then the coordinates of point C are {ccs H, sin til]. {c} Draw the tangent line to the circle at the point {1,0}. Continue this line verti- cally until it crosses the ray you drew in the previous part. Mark the point of intersection H. 53. 1t'rou should now have a picture of a right triangle iii-1.03 sitting in Quandrant l. The intersection of the triangle with the unit circle denes a sector of angle H. [The shape of a sector on the circle is like a slice of pie). {a} 'What is the area of this sectoriIII {b} Based on visual inspection, How does the area of the sector compare to the area of triangle ? {c} Use a straight edge to complete the line segment connecting point FL to point C. 'What type of triangle is 3.00? {d} Based on visual inspection, How does the area of the sector compare to the area of triangle $3150? [-9. {a} Find the area of triangle 3103. {Recall that the coordinates of point C are [cosELsin till]. {b} Given that you know the area of the unit circle is n, nd the area of the sector with angle H. {c} Find the area of triangle 3100. {Recall that the coordinates of point C are {cosIELsin Hi]. {d} 'Write the area of the sector1 the area of 31513, and the area of $3193 in the correct order as an inequality. Tl]. {a} Divide every expression in these inequalities by the area of $3150. (b) Take the reciprocal of every expression and reverse the direction of the inequalities. (c) Use the Squeeze Theorem to calculate lim sing