Sin 2 3. Ex 73 14 Integrate the function cos⁡〖???? − sin⁡???? 〗/(1 + sin⁡2???? ) ∫1 cos⁡〖???? − sin⁡???? 〗/(1 + sin⁡2???? ) ???????? =∫1 cos⁡〖???? −〖 sin〗⁡???? 〗/(???? + 2 sin⁡???? cos⁡???? ) ???????? =∫1 cos⁡〖???? −〖 sin〗⁡???? 〗/(〖????????????〗^????⁡???? + 〖????????????〗^????⁡???? + 2 sin⁡cos⁡???? ) ????????.

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The Sir Isaac Newton (SIN) exam is a test of high school physics and is offered by the Department of Physics & Astronomy at the University of Waterloo to encourage the teaching of physics The exam although challenging is meant to be refreshing and fun Political and other topical humour have marked SIN exams for years Students participate from across Canada.

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Rough We know that cos 60° = 1/2 θ = 60° = 60 × ????/180 = ????/3 Since (−1)/2 is negative Principal value is ???? – θ ie π −????/3 = 2????/3 Solving sin−1 ((−????)/????) Let y = sin−1 ((−1)/2) sin y = (−1)/2 sin y = sin ((−????)/????) Since Range of sin−1 is between [(−????)/2 ” ” ????/2] Hence Principal Value is (−????)/???? Rough We know that sin 30° = 1/2.

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4 # John 844 (2 Cor 113 1 Tim 214) Then the serpent said to the woman “You will not surely die 5 For God knows that in the day you eat of it your eyes will be opened and you will be like God knowing good and evil ” 6 So when the woman # 1 John 216 saw that the tree was good for food that it was pleasant to the eyes and a tree desirable to make one wise she took of its.