Question i. Sketch the graph of the curve , for . The straight line , where is a constant, passes through the maximum point of this curve for . ii. Find the value of k in terms of . iii. State the coordinates of the other point, apart from the origin, where the line and the curve intersect. Solution i. […]
Question i. Show that the equation may be written in the form where . ii. Hence solve the equation , for . Solution i. We have; We need to express the equation in terms of only because we are given that . We have the trigonometric identity; We can write it as; Hence the equation becomes; We can also write it as; Let; […]
Question Find all the values of in the interval which satisfy the equation; Solution First we need to manipulate the given equation to write it in a single trigonometric ratio; Dividing the entire equation by ; Using the relation we can rewrite the equation as, To solve this equation for , we can substitute . Hence, Since given interval is , for interval can […]
Question The diagram shows a semicircle ABC with centre O and radius 8 cm. Angle radians. i. In the case where , calculate the area of the sector BOC. ii. Find the value of for which the perimeter of sector AOB is one half of the perimeter of sector BOC. iii. In the case where , show that the exact length […]