X xc630 Junior Member Joined Sep 1, 2005 Messages 164 Jan 11, 2006 #1 Hello I need some help with this trig problem. In Triangle DEF sec F= -SQRT(2) I have to find the measure of angle F and tan F I used tan^2F +1 = sec^2 F and got tan F as 1. But how would you find the measure of angle F?
Hello I need some help with this trig problem. In Triangle DEF sec F= -SQRT(2) I have to find the measure of angle F and tan F I used tan^2F +1 = sec^2 F and got tan F as 1. But how would you find the measure of angle F?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Jan 11, 2006 #2 Hello, xc630! In triangle DEF, \(\displaystyle \sec F\,=\,-\sqrt{2}\) I have to find the measure of angle \(\displaystyle F\) and \(\displaystyle \tan F\) Click to expand... If the secant of angle F is negative, it must be obtuse. \(\displaystyle \;\;\sec\theta\) and \(\displaystyle \cos\theta\) are negative in quadrant 2. What angle has a secant of -\(\displaystyle \sqrt{2}\) ? \(\displaystyle \sec\theta\:=\:\frac{hyp}{adj}\:=\:\frac{\sqrt{2}}{-1}\;\) (The hypotenuse is always positive.) Using Pythagorus, we find that: \(\displaystyle opp\,=\,1\) Therefore: \(\displaystyle \,\tan F\:=\:\frac{opp}{adj}\:=\:\frac{1}{-1}\:=\:-1\) The angle looks like this. Code: * :\ _ : \√2 : \ θ -+- - - *------- -1 You're expected to know that the angle is \(\displaystyle 135^o\) or \(\displaystyle \frac{3\pi}{4}\) radians.
Hello, xc630! In triangle DEF, \(\displaystyle \sec F\,=\,-\sqrt{2}\) I have to find the measure of angle \(\displaystyle F\) and \(\displaystyle \tan F\) Click to expand... If the secant of angle F is negative, it must be obtuse. \(\displaystyle \;\;\sec\theta\) and \(\displaystyle \cos\theta\) are negative in quadrant 2. What angle has a secant of -\(\displaystyle \sqrt{2}\) ? \(\displaystyle \sec\theta\:=\:\frac{hyp}{adj}\:=\:\frac{\sqrt{2}}{-1}\;\) (The hypotenuse is always positive.) Using Pythagorus, we find that: \(\displaystyle opp\,=\,1\) Therefore: \(\displaystyle \,\tan F\:=\:\frac{opp}{adj}\:=\:\frac{1}{-1}\:=\:-1\) The angle looks like this. Code: * :\ _ : \√2 : \ θ -+- - - *------- -1 You're expected to know that the angle is \(\displaystyle 135^o\) or \(\displaystyle \frac{3\pi}{4}\) radians.
