Everything Maths Grade 10

Effect ofa a > 1 : vertical stretch, amplitude increases  y a= 1 a> 1 0 <a< 1 1 <a< 0 a< 1 a= 1: basic si ...

Period The period ofy=asin+qis 360 °. This means that one sine wave is completed in 360 °. Intercepts They-intercept off() =as ...

Cosine function EMA57 Functions of the formy=cos EMA58 Worked example 18: Plotting a cosine graph QUESTION y=f() =cos [0° ...

Functions of the formy=acos+q EMA59 Investigation: The effects ofaandqon a cosine graph In the equation,y=acos+q,aandqare cons ...

Effect ofa a > 1 : vertical stretch, amplitude increases  y a= 0 a> 1 0 <a< 1 1 <a< 0 a< 1 a= 1: basic co ...

y=f(0°) =acos 0 °+q =a(1) +q =a+q This gives the point(0°;a+q). Worked example 19: Sketching a cosine graph QUESTION Sketch the ...

Comparison of graphs ofy=sinandy=cos EMA5C 30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 220 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦ 1 1 y=cos y= ...

Step 2: Plot the points and join with a smooth curve 30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 220 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦ 3 2 ...

On the same set of axes, plot the following graphs for 0 ° 360 °: 1.y 6 = 2 tan 2.y 7 =tan 3.y 8 =tan 4.y 9 = 2tan Use yo ...

Discovering the characteristics EMA5H Domain and range From the graph we see thattanis undefined at= 90°and= 270°. Therefore ...

Step 3: Plot the points and join with a smooth curve 30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 220 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦ 5 4 ...

3.The graph below shows a trigonometric equation of the following form:y=acos+q. Two points are shown on the graph:Point Aat(18 ...

6.The graph below shows a tangent curve with an equation of the formy=atan+q. Two points are labelled on the curve:Point Ais at ...

9.With the assistance of the table below sketch the three functions on the same set of axes.  0 ◦ 45 ◦ 90 ◦ 135 ◦ 180 ◦ 225 ◦ 2 ...

d) 90 180 270 360 1 2 3 4 5 E y= 2cos+^52 x y 12.State the coordinates atEand the domain and range of the function in the inter ...

a) 90 ◦ 180 ◦ 270 ◦ 360 ◦ 2 2 0  f() b) 90 ◦ 180 ◦ 270 ◦ 360 ◦ 1 2 (^0)  f() 15.For which values ofis the function increas ...

30 60 90120150180210240270300330360 3 2 1 1 y= 2 sin 1 x y 17.For which values ofis the function positive, in the interval ...

90 180 270 360 3 2 1 1 2 3 f(x) g(x) C B D A x y a)State the coordinates atA; B; CandD. b)How many times in this interval doe ...

6.7 Interpretation of graphs EMA5J Worked example 22: Determining the equation of a parabola QUESTION Use the sketch below to de ...

Worked example 23: Determining the equation of a hyperbola QUESTION Use the sketch below to determine the values ofaandqfor the ...