Angles and quadrants

Measure rotations from the positive x-axis: anticlockwise is positive; clockwise is negative. Basic angle The reference angle alpha is the acute angle to the x-axis. The quadrant determines the signs. Degrees and radians 180 =pi rad **Conversion** | **Rule** | **Example** Degrees to radians | Multiply by pi180. | 72 =72 x pi180 = 2pi5 rad Radians to degrees | Multiply by 180 pi. | 3pi4= 34 x 180 =135 90 = 2, 270 = 3pi2, 360 =2pi. Set the calculator to the angle unit used in the question. Signs and quadrants **Quadrant** | **Positive there** | **Angle theta from basic angle alpha** | **Sketch** I | All of sintheta, costheta, tantheta | theta=alpha | II | sintheta (and cosectheta) | theta=180 -alpha theta=pi-alpha | III | tantheta (and cottheta) | theta=180 +alpha theta=pi+alpha | IV | costheta (and sectheta) | theta=360 -alpha theta=2pi-alpha | Negative angles and full revolutions **Situation** | **Rule** | **Example** Negative angle (clockwise turn) | sin(-theta)=-sintheta cos(-theta)=costheta tan(-theta)=-tantheta | cos(-70)=cos70 Beyond one revolution | sin(theta+-360 k)=sintheta cos(theta+-360 k)=costheta tan(theta+-180 k)=tantheta | sin410 =sin50 In the periodic identities, k in Z. Measure the basic angle from the x-axis.