Reference no: EM131008746
Goal: To move that limθ→0 sin (θ) / θ = 1. This limit is essential to proving that the derivative of sin(x) is cos(x).
Rules: You may discuss with other students to work out the answers. llowever you may NOT copy other students' work. You must complete the quiz alone.
The above diagram shows two triangles ΔABD, ΔHED, and a sector 
ABD. The sectorABD is part of a circle centered at A with radius 1. So IABI = IADI = 1.
1. Let L1 = |BC|, and L2=|ED|.
Calculate L1 and L2 in terms of the angle θ.
2. Using L1 and L2, calculate the areas of ΔHED and ΔABD.
3. Calculate the area of the sectorABD in terms of angle θ.
4. Take the formulas you got in 2) and 3) and just by looking at the diagram, put the three areas in order of increasing size.
5. Simplify the inequalities to show that 1 ≥ sin x / x ≥ cos x.
6. Use the Squeeze Theorem to get the final result.
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