Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.33

Use special triangles to determine geometrically the values of sine, cosine, and tangent for $\frac{\pi}{3}$, $\frac{\pi}{4}$, and $\frac{\pi}{6}$, and use the unit circle to express the values of sine, cosine, and tangent for $\pi - x$, $\pi + x$, and $2\pi - x$ in terms of their values for $x$, where $x$ is any real number.

Unpacked Content

Knowledge

Students know:
  • The relationship between the lengths of the sides of a 45-45-90 and 30-60-90 triangle.
  • The basic trig ratios.

Skills

Students are able to:
  • Find the value of sine, cosine, and tangent of π/3, π/4 and π/6 using special triangles.
  • Locate an angle in standard position in the unit circle.
  • Convert between degrees and radians.

Understanding

Students understand that:
  • For an angle in standard position, the point where the terminal ray intersects the unit circle has an x-coordinate which is the value of the cosine of the angle and a y-coordinate which is the value of the sine of the angle.
  • Patterns that can be identified on the unit circle allow for application of right triangle trigonometry to angles of all sizes.

Vocabulary

  • Special triangles
  • Unit circle
ALSDE LOGO