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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:

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Bellwork

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  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

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