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.
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
UP:MA19.PRE.33
Vocabulary
- Special triangles
- Unit circle
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.
