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Finding Reference Angles. It is necessary to be able to make larger angles smaller. We do this by finding reference angles: Step: 1.Start by drawing the.

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Presentation on theme: "Finding Reference Angles. It is necessary to be able to make larger angles smaller. We do this by finding reference angles: Step: 1.Start by drawing the."— Presentation transcript:

1 Finding Reference Angles

2 It is necessary to be able to make larger angles smaller. We do this by finding reference angles: Step: 1.Start by drawing the given angle 2.Now, we determine how many degrees it is until we get to the x-axis (horizon) 3.This is your reference angle 4.A reference angle is always positive Determine the reference angle for 140 degree angle. 40 degrees is the reference angle for 140 degrees A reference angle must be an ACUTE angle!!

3 Determine the reference angle for a 240 degree angle. Determine the reference angle for a 323 degree angle. In the first quadrant, the angles are acute, so no need to find a reference angle.

4 Determine the reference angle for a 470 degree angle. Determine the reference angle for a -125 degree angle.

5 Homework Page 8 & 9 #16,28

6 Applications of reference angles: Express as a function of a positive acute angle: Step: 1.Start by drawing the given angle 2.Find the reference angle 3.Rewrite the function using reference angle 4.Determine SIGN of function in quadrant where it was drawn What is tan in quadrant II? A S C T

7 Express as a function of a positive acute angle:

8 Applications of reference angles: Find the exact value of each expression: Step: 1.Start by drawing the given angle 2.Find the reference angle 3.Rewrite the function using reference angle 4.Determine SIGN of function in quadrant where it was drawn 5.Now find exact value using exact value chart Reference angle Cos in quad II is negative Since cos is negative in quadrant II, then the exact value is negative as well

9 Find the exact value of each expression:

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12 Exact Values of quadrantal angles: We are going to graph four points and use our knowledge of the unit circle to help us! Just use these points to find the sin or cos of any angle falling on that line. y-value is sin

13 Exact Values of quadrantal angles: How do we find tan of these angles? Remember: undefined

14 Homework Page 8 & 9 #8-14,21,24


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