Answer:
Step-by-step explanation:
slope of any line is same as the tan θ . so we first try to find the slope of the given line and then using that we can find remaining trigonometric functions .
To find the slope of a line we need to change the equation of line to slope intercept form .
2y - 5x +16 =0
move all terms to right
2y = 5x - 16
divide all by 2
y = 5/2 x - 8
compare this with y =mx+b
slope = m = 5/2
It means
tan θ = 5/2 = 2.5
tan θ = 2.50
now use the trigonometric ratios (see the image attached )
sin θ = [tex]\frac{y}{z} = \frac{5}{\sqrt{29} } = 0.93[/tex]
cos θ = [tex]\frac{x}{z} = \frac{2}{\sqrt{29} } = 0.37[/tex]
tan θ = 2.50
cot θ = [tex]\frac{x}{y} = \frac{2}{5 } = 0.40[/tex]
sec θ = [tex]\frac{z}{y} = \frac{\sqrt{29}{5} } = 1.08[/tex]
csc θ = [tex]\frac{z}{y} = \frac{\sqrt{29}{2} } = 2.69[/tex]
