LEARN · EXPLAIN · REVISE

Here x is a number of degrees, so the whole angle 4x is measured in degrees. Find the least positive period in degrees. Enter only the number.

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

TOPIC 01

Trigonometric ratios and function graphs

The amplitude 2 and downward translation 3 do not change the period. The radian value π/2 represents the same angular interval but is not the requested numerical unit.

PREDICT → MOVE → EXPLAIN

See amplitude, period and phase together.

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

Try it. Leave your reasoning visible.

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

01 / Foundation#Your turn

Here x is a number of degrees, so the whole angle 4x is measured in degrees. Find the least positive period in degrees. Enter only the number.

y=2\cos((4x)^\circ)-3

Working and explanation

BUILD THE REASONING

Hint 1

Use 360 degrees for one full turn, not 2π.

Hint 2

Find how far x must increase for 4x to increase by 360.

Worked solution

Write the full-cycle condition in degrees.
$4T=360$
Divide by the horizontal multiplier.
$T=\frac{360}{4}=90$

The least positive period is 90°.

Checks and common pitfalls: The amplitude 2 and downward translation 3 do not change the period. The radian value π/2 represents the same angular interval but is not the requested numerical unit.

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