On the unit circle, cosine is the horizontal coordinate and sine the vertical coordinate. Tangent is sine divided by cosine. Their signs therefore follow the signs of coordinates in each quadrant. **Quadrant** | **I** | **II** | **III** | **IV** sin | + | + | − | − cos | + | − | − | + tan | + | − | + | − The reference angle is the acute angle to the x-axis. For 150 =180 -30, sine is positive and cosine negative: sin150 =1/2, cos150 =- 3/2. For 210, both sine and cosine are negative, so tangent is positive. An inverse-trigonometric calculator button usually returns only one principal angle. Use the signs and the stated interval to find all required solutions.

On the unit circle, cosine is the horizontal coordinate and sine the vertical coordinate. Tangent is sine divided by cosine. Their signs therefore follow the signs of coordinates in each quadrant.

The reference angle is the acute angle to the x-axis. For \(150^\circ=180^\circ-30^\circ\), sine is positive and cosine negative: \(\sin150^\circ=1/2\), \(\cos150^\circ=-\sqrt3/2\). For \(210^\circ\), both sine and cosine are negative, so tangent is positive.

An inverse-trigonometric calculator button usually returns only one principal angle. Use the signs and the stated interval to find all required solutions.

Trigonometry

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Reference angles and signs

Reference angles and signs