Question Functions and are defined by for . i. Find the range of . ii. Sketch the graph of . iii. State, with a reason, whether has an inverse. Solution i. We have the function; We can write it as; We know that; Hereby; We can find the range of by substituting extreme possible values of ; Therefore; ii. […]
Question The equation of a curve is . The equation of a line is . On the same diagram, sketch the curve and the line for . Solution First we sketch for . We can find the points of the graph as follows. Now we sketch the line for . We can write it as; Slope-Intercept form of the […]
Question The diagram shows the graph of for . i. Find the values of , and . ii. Find the smallest value of in the interval for which . Solution i. We are given that; When we observe given graph of this function, it is evident that y-intercept of the graph, i.e. when , is 3. Hence for […]
Question The diagram shows a semicircle ABC with centre O and radius 6 cm. The point B is such that angle BOA is 90o and BD is an arc of a circle with centre A. Find i. the length of the arc BD, ii. the area of the shaded region. Solution i. Expression for length of a […]
Question i. Prove the identity . ii. Solve the equation for . Solution i. We have the trigonometric identity; We can rewrite it in two ways; ii. To solve the equation for , we can express, as demonstrated in (i), the right hand side of given equation as; Therefore the given equation can be written as; We have […]
Question Solve the equation for . Solution To solve this equation for , we can substitute . Hence, Since given interval is , for interval can be found as follows; Multiplying the entire inequality with 2; Adding to entire inequality; Since ; Hence the given interval for is . To solve equation for interval , Using calculator we can find the value of . To find all […]
Question Prove the identity Solution We are given the equation; We can rewrite it as; We have the trigonometric identity; We can rewrite it as; Therefore; We have the trigonometric relation; Therefore;