Question

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 = 0
sin θ =
cos θ =
tan θ =
cot θ =
sec θ =
csc θ =

Answer 1

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 = $\frac{y}{z} = \frac{5}{\sqrt{29} } = 0.93$

cos θ =  $\frac{x}{z} = \frac{2}{\sqrt{29} } = 0.37$

tan θ =  2.50

cot θ =  $\frac{x}{y} = \frac{2}{5 } = 0.40$

sec θ =  $\frac{z}{y} = \frac{\sqrt{29}{5} } = 1.08$

csc θ =  $\frac{z}{y} = \frac{\sqrt{29}{2} } = 2.69$