Precalc trig problem?

Posted on 2016-05-04 18:46:00 in Math by LANE

I have a final soon and there's a problem that integrates a cumulation of what we learned through the course. I missed a good chunk for personal reasons, so what I know is patchy. I can't afford a tutor right now, so if you can help in any way that would be appreciated. 

a. graph hyperbola x^2 - x^2 = 1 (use branch w/positive coords.) 
b. consider substitutions for arbitrary t: x= (e^t - e^-t )/2 and y = (e^t + e^-t )/2 

i. show the substitutions satisfy the hyperbolic equation. 
ii. use a new substitution, w = e^t, & suppose at point 'a' the corrdinate is 5. write an eq. that will find w. solve for w. 
iii. using log properties, find t. 
iv. find value of y coord at this point by using iii. 
v. verify that w/ x=5 & answer from (iv) that the point is on the hyperbola. 
vi. the x coordinate is the hyperbolic cosine of t while the y coordinate is the hyperbolic sine. figure a quotient that would give the hyperbolic tangent. simplify as much as possible, preferably to a single fraction. 
vii. using (vi), if your quotient equals 5, find t. 
viii. using (vii), find exact x-y coordinates of this point. 

Thank you in advance.

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