Trig identities: Pythagorean, symmetry and periodicity, and sum and difference
Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.
On Noah's unit circle worksheet, θ is in Quadrant II and sin θ = 3/5. What is cos θ?
Pia's robot ends a turn θ in Quadrant IV with cos θ = 5/13. What is sin θ?
Unit circle: the point (x, y) = (cos θ, sin θ) is in Quadrant IV, and (5/13)² + y² = 1. Unit circle: the point (x, y) = (cos θ, sin θ) is in Quadrant IV, and (5/13)² + y² = 1. Unit circle (x, y) = (cos θ, sin θ) x y θ Quadrant IV (cos θ, sin θ) (5/13)² + y² = 1 On Ren's unit circle worksheet, θ is in Quadrant III and sin θ = -8/17. What is cos θ?
Unit circle: the point (x, y) = (cos θ, sin θ) is in Quadrant III, and x² + (-8/17)² = 1. Unit circle: the point (x, y) = (cos θ, sin θ) is in Quadrant III, and x² + (-8/17)² = 1. Unit circle the point (x, y) = (cos θ, sin θ) Quadrant III x² + (-8/17)² = 1. Tala's robot ends a turn θ in Quadrant II with cos θ = -20/29. What is sin θ?
Unit circle: the point (x, y) = (cos θ, sin θ) is in Quadrant II, and (-20/29)² + y² = 1. Unit circle: the point (x, y) = (cos θ, sin θ) is in Quadrant II, and (-20/29)² + y² = 1. x y Unit circle Quadrant II (x, y) = (cos θ, sin θ) (-20/29)² + y² = 1 Esme's robot ends a turn θ at (-3/5, 4/5) on a unit circle floor grid. Where does a turn of -θ end?
Unit circle with the point for θ, (-3/5, 4/5), and the x-axis drawn as a mirror line. Unit circle with the point for θ, (-3/5, 4/5), and the x-axis drawn as a mirror line. Unit circle x-axis −2 −1.5 −1 −0.5 0.5 1 −2 −1.5 −1 −0.5 0.5 1.5 2 0 θ Kira's robot ends a turn θ at (8/17, -15/17) on a unit circle floor grid. Where does a turn of -θ end?
Unit circle with the point for θ, (8/17, -15/17), and the x-axis drawn as a mirror line. Unit circle with the point for θ, (8/17, -15/17), and the x-axis drawn as a mirror line. Unit circle x-axis −1.5 −1 −0.5 0.5 1 −1.5 −1 −0.5 0.5 1.5 0 θ Luz's robot ends a turn θ at (12/13, 5/13) on a unit circle floor grid. Where does a turn of 90° − θ end?
Unit circle with the point for θ, (12/13, 5/13), and the line y = x drawn as a mirror line. Unit circle with the point for θ, (12/13, 5/13), and the line y = x drawn as a mirror line. Unit circle y = x θ On Milo's unit circle worksheet, the turn θ ends at (3/5, 4/5). Where does the turn 90° − θ end?
Unit circle with the point for θ, (3/5, 4/5), and the line y = x drawn as a mirror line. Unit circle with the point for θ, (3/5, 4/5), and the line y = x drawn as a mirror line. y = x θ Noah's robot ends a turn θ at (-15/17, 8/17) on a unit circle floor grid. Where does a turn of 90° − θ end?
Unit circle with the point for θ, (-15/17, 8/17), and the line y = x drawn as a mirror line. Unit circle with the point for θ, (-15/17, 8/17), and the line y = x drawn as a mirror line. Unit circle y = x θ On Pia's unit circle worksheet, the turn θ ends at (24/25, -7/25). Where does the turn 90° − θ end?
Unit circle with the point for θ, (24/25, -7/25), and the line y = x drawn as a mirror line. Unit circle with the point for θ, (24/25, -7/25), and the line y = x drawn as a mirror line. θ y = x