Question

I need to use the distance formula below to find the exact corordinates of the terminal point of pi/8 from pi/4 and then solve for (b) and then (c ). It has to use the distance formula not half angle formula of cosine and sine. Please include your step by step solution. Thank you.

The point at x/8 is halfway between 0 and x/4. So, if its coordinates are (x,y), then we have d[(x,y),(1,0)) = d[(x,y). (7312, V3/2)) which is to say (x - 1)2 + (y - 0)2 = (x - 72/2) + (y - v3/272 Also, it's on the unit circle, so we get x2 + y2 = 1. Together, you now have two equations in two unknowns to solve. Question 2. (7 marks) In lectures, we determined that the terminal point associated with moving a distance = /4 units from the point (1,0) anti-clockwise around the unit circle, 2 + y = 1, has coordinates (x,y) = (v2/2, 2/2). the result from lectures, modify the analysis that we performed in class to then determine the exact coordinates of the terminal point associated with moving a distance 1 /8 units from the point (1,0) anti-clockwise around the unit circle. () Use your result from part (a), and the symmetry of the unit circle to deduce the coordinates of the terminal points associated with t= .= and t = -1 (e) Hence determine the exact values of: (1) cos (1) (iv) sin ( -75.) + cos (-15)

Answer 1

In af The point (ay) at to it halfway belveen 0 and to دها so, if its coordinals are (x,y) then we have I دردلك لتحاورته: ((ملار (رح)ف ) لح x - 112 + ( 2 - 1 ) = ( x 8) + ( - ( squating hath side, we have عدا عه+توسع ( باسلام وتحتل معتدل و - - - و بعد لاتعدد وقد تحدد عدد ولد+عك عدد "ولدتح(عل-ها عدلت علي علاه ط لقندوره معامله ملالمعمعمعممهملمننه Shut y = (12-1)x un 6 , we have

22 + (-1022 + 2 +1 - 212) 22 + (3- 2 x2 = | 22 (1+ 3 - 2 ) - (4-25) । 2 = 4-22 पारो quad. I 14-252 So , >

4- 2 4 \u-26 4-2- -2.jc -4-25 9-26 _华 1) x14-26 4-26 y - x 4-22 -4-2E LA (6 ) 2 。 。 E - L 2 、L-ME 02E 2

Thus, y = 4-2/2 52-2 1 4 22 2