Question

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(c) The following table tabulates the (r, y) coordinates of terminal points on the unit circle, 2 = 1, determined by arc lengths t measured anti-clockwise around the unit circle starting at (1,0). Terminal point (x,y) (1,0 0 V23 (2 3)/2+v3 T 12 2 2 V3 1 6 2 2 TT 4 2 2 1 T 2 2 V32 2+ V3 5T (2 12 2 2 (0, 1) 2 (i) Identify a combination of two reflections that will transform the terminal point on 117T the unit circle defined by t to the terminal point defined by t 12 Hence 12 determine the (x,y) coordinates of the terminal point defined by t = 12 (ii) Using the information provided in the above table, and your solution to question 3 (c) (i, determine exact values for (a) sin (B) cos 12 11T tan 12

Answer 1

Please see the attached image. It is well explained
(cos , sine) sin COS

The unit carcle allows us to extend the domain of sine and cosine to all real numbers. The process for determining the sive / Cosine of any angle o is as follows - 1. Starting from (1,0), move along the unit Circle in counterclocknesse direction until the angle that is formed between your position, the origin. and the positive x-axis is equal to O. 2 Sino) is equal to y-coordinate of your point and coso is equal to n-Coordinate- (The other trigonometric function found by using relation of can also be sine and Cosine soln: - انا (-x, y) / 2 d* 9 tz-(x non vos Not D3, (2-53# 216 ) ),t=1 - 100 tao 26, for transforming - The to t= - 11/12 Step 1 - reflect with respect to vertical - axis; ie (point 1 point 2) (x, y) – (-x, y) step 2:- reflect again the new wordinate to worit x-axis (point 2 point3 (-u,y) - (x,y)

the value of Finally point 3 we and will get t = - 11T $0., Coordinate will (x,y) 2+ √5 - (2-3) 2+13) 2 (a) sin II sin t bezain = (y-coordinat at t= Tv ) 12 √2+3 (b) Cos I = (x-coordinate at t-T/ - V2 +53 es tan l-111 ) = sin(-1/2) Cost-11T2) - - (2-13) (2+3 l 3/2 = 2-3 Ans,