What is the exact value of the trigonometric expression?
State your answer in simplified radical form and please show all work thank you
What is the exact value of the trigonometric expression?
Hello lovesosa12!
\(\color{BrickRed}\frac{tan(-\frac{7\pi}{6})}{sec(\frac{7\pi}{4})}-sin(\frac{\pi}{2}) \\ =\frac{tan(-210°)}{sec(315°)}-sin(90°)\\ =\frac{tan(-30°)}{sec(45°)}-sin(90°)\\ =\frac{-\frac{\sqrt{3}}{3}}{\sqrt{2}}-1\)
\(=-\frac{\sqrt{3\cdot 2}}{3}-1\\ =-(\frac{\sqrt{6}}{3}+1)\)
\(\Large\frac{tan(-\frac{7\pi}{6})}{sec(\frac{7\pi}{4})}-sin(\frac{\pi}{2})=-(\frac{\sqrt{6}}{3}+1)=-1.81649658\)
!