Problem #3 Catch the mistakes if there is any below. What mistakes were made? Explain using complete sentences. Note there might be no mistakes, one mistakes or several. Check the whole thing. a)...

Problem #3 Catch the mistakes if there is any below. What mistakes were made? Explain using complete sentences. Note there might be no mistakes, one mistakes or several. Check the whole thing. a) Simplify the expression (cosA - cosB)2 + (sinA-sinB)2 Solution: Expand by squaring: cos A-2cosAcosB + cos B + sin2A- 2sinAstnB+ sin B Regroup: cos A+sin2A+cos B +sin B-2sinAsinB-2cosAcosB Use Pythagorean identity: 1+ 1- 2sinAsinB - 2cosAcosB Factor a 2: 2(1-sinAsinB-cOSAcosB) Simplify: 2( 1-sinAB - cosAB) b) Simplify the expression (sinA-sinB)(coSA+cosB) Solution Foil: sinAcOSA+sinAcosB- sinBcoSA - sinBcosB Cancel: sinAcosA-sinBcosB Use the product to sum identity (sinCA +A) + sin(A -A)- sin(B +B)+ sin(B - B) Simplify: sin(24)-sin(2B) Simplify: sinA - sinB Points Problem 1: 10 pts Problem 2: a) 10pts b) 9 pts c) 9 pts Problem 2 a)6 pts b)6 pts Total points :50 Project #3 Trigonometric Identities-please do in separate piece of paper and show your work clearly. Problem1 The path traveled by an object (neglecting air resistance) that is projected at an initial height of ho feet an initial velocity of vo feet per second and an initial angle 8 is given by -16 vo cos20 Where x is the horizontal distance in feet and y is the height in feet. Find the formula for the maximum height of an object projected from ground level at velocity vo and angle 8. The total horizontal distance the object travels is 32 The maximum height happens at half this distance. Substitute it for the x in the general model for the path of a projectile and leave your answer using sine function. Problem#2 The tide or depth of the ocean near the shore changes throughout the day. The water depth d ( in feet) of a bay can be modeled by d = 35-28 cos t 6.2 Where t is the time in hours, with t 0 corresponding to 12:00 am. a) Algebraically find the times in a day at which the high and low tides occur. Write time at hours minutes am or pm (not military time) Algebraically (if possible) find the times at which the water depth is 30 ft Algebraically (if possible) find the times at which the water depth is 3.5 ft b) c)