Q:

Find the approximate values of the trigonometric functions of θ given the following information. Enter the values correct to 2 decimal places. θ is in standard position the terminal side of θ is in quadrant III the terminal side is parallel to the line 2y - 5x + 16 = 0sin θ = cos θ = tan θ = cot θ = sec θ = csc θ =

Accepted Solution

A:
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 =  2.50cot 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]