Angle Between Lines

Linear Functions – Angle Between Lines

If the acute angle \( \theta \) between two straight lines \( y = m_1 x + A \) and \( y = m_2 x + B \), then
$$\tan{\theta} = \left|\frac{m_1 – m_2}{1+m_1 \times m_2}\right|$$

Basic of Angle Between Lines

Find the acute angles between the lines \( y = -2x + 4 \) and \( y = 3x + 2 \), giving your answer to the nearest degree.

Gradients for Angle Between Lines

Find the acute angles between the lines \( 2y = x + 1 \) and \( 2x – 3y = 4 \), giving your answer to the nearest degree.

The Nearest Minute for Angle Between Lines

Find the acute angle between the lines \( 2x+y+1=0 \) and \( x+y+4=0 \), correcting to the nearest minute.

Two Points for Angle Between Lines

Find the acute angle between the line \( 2x-5y+1=0 \) and the line joining \( (-1,2) \) and \( (5,3) \), correcting to the nearest minute.

Angle Between Lines of Intersection of Exponential Graphs

Find the angle between the tangents drawn to the curve \( y_1 = e^{x} \) and \( y_2 = e^{-x} \) at their point of intersection.

Angle Between Lines of intersection of Trigonometric Graphs

Find the acute angle between the curves \( y_1 = \sin{x} \) and \( y_2 = \sin{2x} \), at their point of intersection, where \(0 \lt x \lt 180^{\circ} \), correcting to the neatest degree.

Angle Between Lines for Finding Gradients

The acute angle between the lines \( 2x-y-7=0 \) and \(y=mx+3 \) is \( 25^{\circ} \), find the value(s) of \(m\), correct to 1 decimal place.