@ Recall that to find a resultant vector, we add like components. If v = v1i+ v2j and w = wli + lvzjI then it + w 2 (v1 + w1}i + (v; + w2}j. Hence, the resultant vector u can be found as follows. (Round your answers to five decimal places.) u:u1+U2+IJ3 [4 cos(160}i + 4 sin[1600)j] + [F cos(26[i}i + I\" sin[260)j] + [6 cos(15]i + 6 sin(15]j] [4 cos(1609} + ? cos(260] + I5 cos(15}]i + [4 sin(16)+ T sin(26i} + 6 sin(15)]j (4 cos(1600}+ ? cos{260] + 5 cos(15}, 4 sin(16i]\") + ? sin(260) + s sin[15}) x The vector u above is the resultant vector from the man's home to the end of his walk. Recall that the magnitude of a vector can be found by using the formula \"V\" = u' v17 + v22- The magnitude of vector u can be found as follows. 2 Ill-ll = \\/( E) + (W:- at : [Rounded to two decimal places.) Hence, when rounded to two decimal places, the man is approximately : miles from his home. Submit gyou cannot come back). 2. [0/3 Points] DETAILS PREVIOUS ANSWERS OSPRECALC1 7.5.246. Find all exact solutions on [0, 2x). (Enter your answers as a comma-separated list.) 2 cost = 1 8 = O X If necessary, isolate the cosine function on one side of the equation. Using the unit circle, what Additional Materials eBook Solving Trigonometric Equations IV8. [2/4 Points] PREVIOUS ANSWERS OSPRECALC18.8.561. ASK YOUR TEACHE An airplane is heading nolth at an airspeed of 700 krn/hr, but there is a wind blowing from the southwest at 60 krn/hr. How many degrees off course will the plane end up flying? (Round vour answer to three decimal places.)- 0 05? x 5 east of north What is the plane's speed relative tn the ground? (Round yCILll answer tn the nearest whole number.) MBGBE J kmfhr t Begin by drawing a pittui'e nfthe problem, with vettnrs representing the velocity of the plane and of the wind. By placing the initial point of the wind vector at the terminal point of tile plane's vector, vector addition can be used so that th- the plane's new speed and direction as a result of the wind. What is the length of the unknown side of the obtuse triangle that results from adding the plane's velocity vector to the Wind's velocity vector? How can the Law 0f Cesines be us Sines then be used to nd the angle that the plane is blown off course? Additional Materials 4. [-/6 Points] DETAILS OSPRECALC1 7.5.251.TUT.SA. MY NOTES ASK YOUR TEACHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find all exact solutions on [0, 27). 2 sin(x) cos(x) - sin(x) + 2 cos(x) - 1 = 0 Step 1 of 4 In order to solve the equation, we use the zero-product property and completely factor its left-hand side. Notice the common factor in the first two terms is Apply the Distributive property in reverse to factor the first two terms in the equation. 2 sin(x) cos(x) - sin(x) + 2 cos(x) - 1 = 0 sin (x) (2 cos ( x) - 1) + 2 cos ( x ) - 1 = 0 Notice now there are two terms on the left-hand side of the equation and the common factor of these two terms is Submit Skip (you cannot come back)8. [014 Points] FREVIOUSANSWERS OSPRECALC'I 7.5.287. ASK YOUR TEACHER Find all solutions on the interval [0, 2n}. Look for opportunities to use ti'igonometri: identities. (Enter your answers as a :Dmmarseparated list. Round your answers to four decimal places. If an answer does not exist, enter DNE.) 12 shim + c0503. 5 r: 2.30052= 2300520322734. 07221734 1 X Retail the method of solving equations that are quadratic in form and the Pythagorean identity involving Sine anti cosine. If the substitution (053) : u were made, how would the equation be factored and subsequently solved? Additional Materials E] eBouk E Soiving Trigonometric Equations il E Soiving Trigonometric Equations ill E Solving Trigonometric Equations VI