SOLUTION: How do you find tan theta if cos theta = -0.99619470 and theta is in QII using fundamental IDs of Trig Functions? I want to learn how to do it, not just the answer because I can't

Algebra ->  Trigonometry-basics -> SOLUTION: How do you find tan theta if cos theta = -0.99619470 and theta is in QII using fundamental IDs of Trig Functions? I want to learn how to do it, not just the answer because I can't      Log On


   

Question 575442: How do you find tan theta if cos theta = -0.99619470 and theta is in QII using fundamental IDs of Trig Functions? I want to learn how to do it, not just the answer because I can't even get started. Thanks.
Mark
Answer by KMST(5399) About Me  (Show Source):
You can put this solution on YOUR website!
You need a trigonometric identity. Either you find trigonometric identities from some source, or you deduce the ones you do not remember from the ones you do remember. You can search for "trigonometric identities" on the internet and will find them in many sites, including Wikipedia.
I do not believe in memorizing, but unfortunately I have not been able to convince teachers.
I remember the fact that
cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1 --> sin%28theta%29=sqrt%281-cos%5E2%28theta%29%29 for QI and QII (For angles in the third and fourth quadrants I have to put a minus sign in front of the square root, but in QI and QII, sine is positive).
So substituting into the definition of tangent,
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29, which I also remember, I get
tan%28theta%29=sqrt%281-cos%5E2%28theta%29%29%2Fcos%28theta%29
Now that I found my trigonometric identity, it's just plug and chug:
tan%28theta%29=sqrt%281-%28-0.99619470%29%5E2%29%2F%28-0.99619470%29=-0.087489
I would not write more digits because the next digit varies if I use -0.99619471 or -0.99619469 for cos%28theta%29