LEARN · EXPLAIN · REVISE

Using the displayed bracketed form and radians, how is this graph obtained from y = 2 sin x?

Read the idea, work independently, then explain what changed.

TOPIC 01

Trigonometric ratios and function graphs

At x = π/4 the angle inside sine is zero and the output is 1. This checks the direction of both translations.

PREDICT → MOVE → EXPLAIN

Predict the number of cycles and the horizontal shift. Switch angle units without changing the curve.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

y=2\sin\left(x-\frac\pi4\right)+1

Working and explanation

BUILD THE REASONING

Hint 1

The expression x − h means the original graph is shifted right by h.

Hint 2

The +1 is outside sine, so it changes every output by the same amount.

Worked solution

Match the angle to x − h.
$h=\frac\pi4$
Read the vertical translation and check a reference point.
$(0,0)\longmapsto\left(\frac\pi4,1\right)$

D: shift right by π/4 and up by 1.

Checks and common pitfalls: At x = π/4 the angle inside sine is zero and the output is 1. This checks the direction of both translations.

Think first. Reveal a hint when the class is ready.