{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

TrigRevWorksheet - Math 1205 Trigonometry Review We begin...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 1205 Trigonometry Review We begin with the unit circle. The definition of a unit circle is: x 2 + y 2 = 1 where the center is (0, 0) and the radius is 1. An angle of 1 radian is an angle at the center of a circle measured in the counterclockwise direction that subtends an arc length equal to 1 radius. Notice that the angle does not change with the radius. There are approximately 6 radius lengths around the circle. That is, one complete turn around the circle is 2 ! " 6.28 radians.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Define the Sine and Cosine functions: Choose P ( x , y ) a point on the unit circle where the terminal side of ! intersects with the circle. Then cos ! = x and sin ! = y . We see that the Pythagorean Identity follows directly from these definitions: x 2 + y 2 = 1 (cos ! ) 2 + (sin ! ) 2 = 1 we know it as: sin 2 ! + cos 2 ! = 1 Example 1. Example 2. Determine: Determine: sin(90 ° ) and cos(90 ° ) sin(3 ! ) and cos(3 ! ) Recall that 90 ° corresponds to ! 2 radians . (How many degrees do 3 ! radians correspond to?) We can read the answers from the graphs: sin(90 ° ) = sin ! 2 " # $ % & = y coordinate of P = 1 sin(3 ! ) = sin(540 ° ) = y coordinate of P = 0 cos(90 ° ) = cos ! 2 " # $ % & = x coordinate of P = 0 cos(3 ! ) = cos(540 ° ) = x coordinate of P = " 1 Problems 1 and 2: 1. Locate the following angles on a unit circle and find their sine and cosine. a. ! 5 " 2 b. 5 ! 2 c. 360 ° d. ! " 2. Given: cos ! = 0 and sin ! = 1 . Find the following: a. the smallest positive ! that satisfies the given equalities. b. one other ! that satisfies the given equalities. Note: ! 1 and ! 2 should be in radians.
Image of page 2
There are six trigonometric functions. We have considered the sine and cosine functions. We can define the four remaining in terms of these functions. The tangent function: tan ! = sin ! cos ! The cotangent function: cot ! = cos ! sin ! The cosecant function: csc ! = 1 sin ! The secant function: sec ! = 1 cos ! We know all of the above functions will have points of discontinuity where the denominator is zero. The graphs of these functions all have vertical asymptotes at these points.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
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