1 / 12

Bellwork

Bellwork. Objectives. You will be able to use reference angles to evaluate the trig functions for any angle. You will be able to locate points on a unit circle and use symmetry to locate other points. Vocabulary. Reference Angle (with examples). Reference Angles. To find a reference angle:

zytka
Télécharger la présentation

Bellwork

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bellwork

  2. Objectives • You will be able to use reference angles to evaluate the trig functions for any angle. • You will be able to locate points on a unit circle and use symmetry to locate other points.

  3. Vocabulary • Reference Angle (with examples)

  4. Reference Angles • To find a reference angle: • Begin by visualizing the angles, and the quadrant in which it terminates. • Figure out the distance from the terminal side to the x-axis. • Here are some rules to figure out how to calculate the reference angle, based on the original angle:

  5. Take it to the UNIT CIRCLE • ON THE UNIT CIRCLE OLNY • X = Cos • Y = Sin • Tan = Y/X KFC

  6. Reference Angles • Then, you can calculate the sine, cosine, tangent, etc. (based on what the problem is asking), by calculating the same trig ratio of the reference angle. • Make sure the sign is right, based on what quadrant you’re working in. • Quadrant 1: All are Positive (both)Quadrant 2: Sine is Positive (y)Quadrant 3: Tangent is Positive (neither)Quadrant 4: Cosine is Positive (x) • ASTC: All Students Take Classes

  7. Reference Angles • Here is an example problem: • Figure out the reference angle. • Determine which quadrant you’re in: 4th quadrant Calculate sin, cos, and tan of the reference angle. • Change the signs. (ASTC – Cosine is positive)

  8. Reference Angles Practice • Using reference angles, evaluate sin θ for each of the following angles. • θ= 135 • θ= 300 • θ= -45

  9. Symmetry • Any time we figure out a point on the unit circle, we can then figure out three other points, just based on symmetry! • Remember which coordinate values (x and y) are positive in negative in the different quadrants. • Example: we have the point ,which is on the unit circle. Determine which quadrant it’s in, andusing symmetry, calculate three otherpoints. • Solution: this is in the 3rd quadrant, so we can use the unit circle to the right to find three other points.

  10. Symmetry Practice • We know that is a point on the unit circle. Using symmetry, find three other points. • Because x is negative, this point must be in the 2nd quadrant. • These points must also be on the unit circle. 3rd Quadrant… 4th Quadrant… 1st Quadrant…

  11. Homework • p. 539, #31-41 odd, 47-54 allp.550, #19-22 all • Due TOMORROW

More Related