SP#7: Unit Q Concept 2: Finding All Trig Functions when given one Trig Function and Quadrant ( Using Identities)

This SP7 was made in collaboration with Daisy Larco. Please visit her awesome posts on her blog by going here.

1.) Finding all trigs by using identities.

In the first step the first thing we need to do is to see what quadrant the trig function will lie in.

So, in this case it lie in the second quadrant because that is the only place where tangent is negative and sine is positive.

The second step is to find all the trig functions by using the identities. So we know that tangent is -5/7, so we can solve for cotangent. Then we plug in the given trig for tangent and simplify to find cotangent. Once we got tangent we can solve for secant, by using 1+tan^2 theta = sec^2. Then plug in tangent and simplify to get secant. Next we solve for cosine, because we already have secant. We just need to plug in the formula cosine theta = 1/ secant theta. Then solve for cosecant, by plugging cotangent in the formula 1= cot^2 theta = csc^2 theta. That will get us cosecant. Then the only thing left we need to find is sine. Just by plugging in cosecant into the formula sin theta = 1/csc theta. This will help you find theta.

2.) Finding all trig by using SOHCAHTOA.

In order to find all the trig values, we must use SOHCAHTOA. Sine = opposite/hypotenuse, y/r. Cosine = adjacent/hypotenuse, x/r. Tangent = opposite/adjacent, y/x. Cosecant = hypotenuse/opposite, r/y. Secant = hypotenuse/adjacent, r/x. Cotangent = adjacent/opposite, x/y.