Question

find the slope of a line

Answer 1

What we know:

y=mx+c

m=tan θ

a) 30°

m=tan  30° =$\frac{1}{\sqrt{3}}$

b)45°

m=tan 45°=1

c)60°

m= tan 60°=$\sqrt{3}$

d)15°

m=tan 15°= tan $\frac{30}{2}$ degrees=$\frac{1- cos 30°}{sin 30°}$=$\frac{1-\frac{1}{2} }{\frac{\sqrt{3} }{2} }$=$\frac{\frac{1}{2} }{\frac{\sqrt{3} }{2} }$=$\frac{1}{\sqrt{3} }$

d)75°

m=tan 75°= tan ( 30° +45°) degrees=$\frac{tan 30+tan45}{1-tan30tan45}$=$\frac{\frac{1}{\sqrt{3} }+1 }{1-\frac{1}{\sqrt{3} } }$  = $\frac{1+\sqrt{3} }{\sqrt{3}-1 }$