Pre-Calc Exam Notes 34

Pre-Calc Exam Notes 34 - 34 Chapter 1 Right Triangle...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
34 Chapter 1 Right Triangle Trigonometry §1.5 Rotating an angle θ by 90 in the clockwise direction results in the angle θ 90 . We could use another geometric argument to derive trigonometric relations involving θ 90 , but it is easier to use a simple trick: since formulas (1.4) (1.6) hold for any angle θ , just replace θ by θ 90 in each formula. Since ( θ 90 ) + 90 = θ , this gives us: sin ( θ 90 ) = − cos θ (1.7) cos ( θ 90 ) = sin θ (1.8) tan ( θ 90 ) = − cot θ (1.9) We now consider rotating an angle θ by 180 . Notice from Figure 1.5.4 that the angles θ ± 180 have the same terminal side, and are in the quadrant opposite θ . x y θ + 180 θ 180 ( x , y ) ( x , y ) θ 180 180 r r (a) QI and QIII x y θ + 180 θ 180 ( x , y ) ( x , y ) θ 180 180 r r (b) QII and QIV Figure 1.5.4 Rotation of θ by ± 180 Since ( x , y ) is on the terminal side of θ ± 180 when ( x , y ) is on the terminal side of θ , we get the following relations, which hold for all
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern