AI generatedAlgebraGCSE Higher

Recognising the tangent graph

Use degrees, its period and vertical asymptotes.

  • Check axis labels and scales before reading values.
  • Use key points and the correct curve shape. Join a curved graph smoothly.
  • An asymptote is approached; do not join separate branches across it.

Example 1

Identify the period from the tan graph. Then use degree mode on a calculator to evaluate to 2 d.., or state if it is undefined.

Coordinate graph−360−270−180−9090180270360−4−3−2−112340
Angles are in degrees. The period is 180°. Vertical asymptotes occur at 90° + 180°. The pattern repeats beyond the displayed window; use the calculator for the final numerical value.
Period: 180°. (to 2 d..).

Example 2

Identify the period from the tan graph. Then use degree mode on a calculator to evaluate to 2 d.., or state if it is undefined.

Coordinate graph−360−270−180−9090180270360−4−3−2−112340
Angles are in degrees. The period is 180°. Vertical asymptotes occur at 90° + 180°. The pattern repeats beyond the displayed window; use the calculator for the final numerical value.
Period: 180°. (to 2 d..).

Your turn

Question 1

Identify the period from the tan graph. Then use degree mode on a calculator to evaluate to 2 d.., or state if it is undefined.

Coordinate graph−360−270−180−9090180270360−4−3−2−112340
Check answer
Angles are in degrees. The period is 180°. Vertical asymptotes occur at 90° + 180°. The pattern repeats beyond the displayed window; use the calculator for the final numerical value.
Period: 180°. (to 2 d..).
Question 2

Identify the period from the tan graph. Then use degree mode on a calculator to evaluate to 2 d.., or state if it is undefined.

Coordinate graph−360−270−180−9090180270360−4−3−2−112340
Check answer
Angles are in degrees. The period is 180°. Vertical asymptotes occur at 90° + 180°. The pattern repeats beyond the displayed window; use the calculator for the final numerical value.
Period: 180°. (to 2 d..).
Question 3

Identify the period from the tan graph. Then use degree mode on a calculator to evaluate to 2 d.., or state if it is undefined.

Coordinate graph−360−270−180−9090180270360−4−3−2−112340
Check answer
Angles are in degrees. The period is 180°. Vertical asymptotes occur at 90° + 180°. The pattern repeats beyond the displayed window; use the calculator for the final numerical value.
Period: 180°. (to 2 d..).
Question 4

Identify the period from the tan graph. Then use degree mode on a calculator to evaluate to 2 d.., or state if it is undefined.

Coordinate graph−360−270−180−9090180270360−4−3−2−112340
Check answer
Angles are in degrees. The period is 180°. Vertical asymptotes occur at 90° + 180°. The pattern repeats beyond the displayed window; use the calculator for the final numerical value.
Period: 180°. (to 2 d..).
Question 5

Identify the period from the tan graph. Then use degree mode on a calculator to evaluate to 2 d.., or state if it is undefined.

Coordinate graph−360−270−180−9090180270360−4−3−2−112340
Check answer
Angles are in degrees. The period is 180°. Vertical asymptotes occur at 90° + 180°. The pattern repeats beyond the displayed window; use the calculator for the final numerical value.
Period: 180°. (to 2 d..).
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