Question i. Show that the equation can be expressed as Where ii. Hence solve the equation for . Solution i. We are given the equation; We have the trigonometric identity; From this we can substitute in above equation; Let ; ii. We are required to solve the equation for […]
Question a) Given that x > 0, find the two smallest values of x, in radians, for which . Show all necessary working. b) The function is defined for . i. Express f(x) in the form , where a and b are constants. ii. Find the range of f. Solution a) We […]
Question The diagram shows a sector OAC of a circle with centre O. Tangents AB and CB to the circle meet at B. The arc AC is of length 6 cm and angle radians. i. Find the length of OA correct to 4 significant figures. ii. Find the perimeter of the shaded region. iii. […]
Question i. Given that , show, without using a calculator, that . ii. Hence, showing all necessary working, solve the equation for Solution i. We are given that; Since ; We have the trigonometric identity; From this we can write; Therefore; Let ; Now we have two options. Since ; We […]
Question The functions is defined for , where and are positive constants. The diagram shows the graph of y = f(x). i. In terms of and state the range of . ii. State the number of solutions of the following equations. a) […]
Question The diagram shows triangle ABC which is right-angled at A. Angle radians and AC = 8 cm. The points D and E lie on BC and BA respectively. The sector ADE is part of a circle with centre A and is such that BDC is the tangent to the arc DE at D. i. […]
Question The equation of a curve is and the equation of a line is . i.State the smallest and largest values of y for both the curve and the line for . ii.Sketch, on the same diagram, the graphs of and for . iii.State the number of solutions of the equation for . Solution i. […]
Question Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants. A curve is such that . The point P (2,9) lies on the curve. i. Show that a2 +b2 has a constant value for all values of x. […]
Question The functions f is defined by for , i. State the range of . ii. Sketch the graph of . The functions g is defined by for , where is a constant. iii. State the largest value of for which g has an inverse. iv. For this value of , find an […]
Question i. Prove the identity ii. Hence solve the equation for Solution i. First, we are required to show that; Since ; We have the trigonometric identity; From this we can write; Therefore; We have the algebraic formula; ii. We are required to solve the equation; For . […]
Question a) Solve the equation for . b) The diagram shows part of the graph of , where is measured in radians and and are constants. The curve intersects the x-axis at and the y-axis at . Find the values of and . Solution a) We are required to solve the equation for […]