Find the exact values of the six trigonometric functions of θ if θ is in standard position and the terminal side of θ is in the specified quadrant and satisfies the given condition.
iii; parallel to the line
5y − 2x + 1 = 0

So the equation of the line is .

Let's put that in standard form (by solving for y):


~ we added 2x and subtracted 1 from both sides
~ divide both sides by 5

So now we have it in the standard form which is .

The gives us the slope. Recall that slope is rise over run.

So the slope is , which means that you could draw a triangle with a rise of 2 and a run of 5.

That's almost enough information to find the trig values, but we still need to know the hypotenuse. Well, thanks to the magic of the Pythagorean Theorem:



Alright, now that we know all three sides, we can find the values.

The "rise" (vertical) or opposite: 2
The "run" (horozontial) or adjacent: 5
The hypotenuse: 

Remember SOHCAHTOA. In order from that mnemonic: 

sin(θ) = opposite over hypotenuse = 

cos(θ) = adjacent over hypotenuse = 

tan(θ) = opposite over adjacent =

Now the others (cosecant, secant, and cotangent) are just the reciprocals (upside-downs) of the others. Remember that cosecant comes first (since sine comes first in the "usuals".

csc(θ) =

sec(θ) =

cot(θ) =

We don't have to 'solve' (approximate) that square root in any of the answers since the problem asked for the exact solution.

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