Trigonometry · Guided Practice

Trig Graphs

8 questions with answers and video solutions. Try each one before revealing the answer.

1
2015 P1 Q6
2 Marks

Part of the graph of y=asin⁡bx∘\displaystyle y=a\sin bx^\circ is shown in the diagram.

Graph of y=a sin bx

State the values of a\displaystyle a and b.\displaystyle b.

2
2018 P1 Q6
2 Marks

Part of the graph of y=acos⁡bx∘\displaystyle y=a\cos bx^{\circ} is shown in the diagram.

Graph of y=a cos bx

State the values of a\displaystyle a and b.\displaystyle b.

3
2019 P1 Q13
2 Marks

Part of the graph of y=3cos⁡(x+45)∘\displaystyle y=3\cos(x+45)^{\circ} is shown in the diagram.

Graph of y=3cos(x+45)

The graph has a minimum turning point at A.
State the coordinates of A.

4
2021 P1 Q13

The graph of y=a cos x∘+b\displaystyle y=a\ cos\ x^\circ +b, 0≤x≤360\displaystyle 0\leq x\leq 360, is given.

Graph of y=a cos x + b

State the values of a\displaystyle a and b.\displaystyle b.

No hints on this one — its full written solution is with the answer.

5
2022 P1 Q8
(1, 1)2 Marks

Part of the graph of y=asin⁡bx∘\displaystyle y=a\sin bx^{\circ} is shown in the diagram.

Graph of y=a sin bx

(a)  State the value of a\displaystyle a.
(b)  State the value of b\displaystyle b.

6
2023 P1 Q13
(1, 1)2 Marks

Part of the graph of y=cos⁡(x+a)∘+b\displaystyle y=\cos(x+a)^\circ + b is shown.

Graph of y=cos(x+a)+b

(a)  State the value of a.\displaystyle a.
(b)  State the value of b.\displaystyle b.

7
2024 P1 Q8
(1, 1)2 Marks

The graph of y=acos⁡bx∘\displaystyle y=a\cos bx^{\circ}, 0≤x≤360\displaystyle 0\le x\le360, is shown.

Graph of y=a cos bx

(a)  State the value of a.\displaystyle a.
(b)  State the value of b.\displaystyle b.

8
2025 P1 Q8
2 Marks

Part of the graph of y=2sin⁡(x−30)∘\displaystyle y=2\sin(x-30)^{\circ} is shown in the diagram.

Graph of y=2sin(x-30)

The graph has a maximum turning point at A.
State the coordinates of A.

Keep practising

More trig graphs questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.