Trigonometric graphs

Sketch the graph of y = 8^x. Indicate any values where the graph crosses the axes.

Sketch the graph of y = cos x for 0 ° ⩽ x ⩽ 360 °. Indicate any values where the graph crosses the x-axis.

The graph of y = 3^x is sketched below.

On the same axes, sketch the graph of y = 2^x.

Charlie sketches this graph.

Charlie says

The equation of my graph is y = sinx.

Explain how you know that Charlie is not correct.

Write down a possible equation for Charlie’s graph.

Sketch the graph of y = 5^x indicating any values where the graph crosses the axes.

Sketch the graph of y = tan x for 0 ° ⩽ x ⩽ 360 ° indicating any values where the graph crosses the axes.

Sketch the graph of y = cos x - 1 for 0 ° ⩽ x ⩽ 720 °.

Sketch the graph of y = sin x for 0 ° ⩽ x ⩽ 360 °.

The graph of y = cos (x - 30) for 0 ° ⩽ x ⩽ 360 ° crosses the x-axis in two places.

Write down the values of x where this occurs.

Sketch the graph of y =- sin x for 0 ° ⩽ x ⩽ 360 °.

Sketch the graph of y = cos x + 1 for 0 ° ⩽ x ⩽ 720 °.

Explain why the equation cos x + 1 = 2.7 has no solutions.

Sketch the graph of y = sin x for 0° ⩽ x ⩽ 360°.

Solve the equation 5 sin x = - 3. Give all of the solutions in the range 0° ⩽ x ⩽ 360°.

(b) x =........ ° or x =........ °