LEARN · EXPLAIN · REVISE

Convert 150° to radians. Use its position on the unit circle to find its exact sine.

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

TOPIC 01

Trigonometric ratios and function graphs

Reflection across the vertical axis preserves the sine value and changes the sign of cosine. A negative sine here would place the point below the horizontal axis.

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#Worked example

Convert 150° to radians. Use its position on the unit circle to find its exact sine.

\theta=150^\circ

Working and explanation

BUILD THE REASONING

Hint 1

Multiply the degree measure by π/180.

Hint 2

The angle is in quadrant II, with reference angle 30°. Sine is positive there.

Worked solution

Use the degree-to-radian conversion.
$150^\circ=150\cdot\frac{\pi}{180}=\frac{5\pi}{6}\ \text{rad}$
Reflect the unit-circle point across the vertical axis.
$\sin150^\circ=\sin(180^\circ-30^\circ)=\sin30^\circ$
Read the exact vertical coordinate.
$\sin\frac{5\pi}{6}=\frac12$

150° = 5π/6 radians, and its sine is 1/2.

Checks and common pitfalls: Reflection across the vertical axis preserves the sine value and changes the sign of cosine. A negative sine here would place the point below the horizontal axis.

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