Angles that straight lines make with the x-axis
Angles that straight lines make with the x-axis
IP 2
7 marks
A straight line through the origin with positive gradient \(m\) makes an acute angle \(\theta\) with the positive \(x\)-axis.
- By considering the point on the line where \(x=1\), explain why \(\tan\theta=m\).[2]
- Find the acute angle between the lines \(y=2x\) and \(y=\dfrac{1}{2}x\).[3]
- A student says that the line \(y=2x\) makes twice the angle with the \(x\)-axis that \(y=x\) makes. Show that the student is wrong.[2]
Solution:
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Answer:(a) The triangle with vertices \((0,0)\), \((1,0)\), \((1,m)\) gives \(\tan\theta=m\) (b) \(36.9^\circ\) (c) \(63.4^\circ\ne2\times45^\circ\)
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