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**Finding Reference Angles**

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**It is necessary to be able to make larger angles smaller**

It is necessary to be able to make larger angles smaller. We do this by finding reference angles: Step: Start by drawing the given angle Now, we determine how many degrees it is until we get to the x-axis (horizon) This is your reference angle 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!!

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**Determine the reference angle for a 240 degree angle.**

In the first quadrant, the angles are acute, so no need to find a reference angle.

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**Determine the reference angle for a 470 degree angle.**

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Homework Page 8 & 9 #16,28

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**Applications of reference angles:**

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

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**Express as a function of a positive acute angle:**

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**Applications of reference angles: Step: **

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

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**Find the exact value of each expression:**

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**Find the exact value of each expression:**

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**Find the exact value of each expression:**

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**Exact Values of quadrantal angles:**

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

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**Exact Values of quadrantal angles:**

Remember: How do we find tan of these angles? undefined undefined

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

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A. Calculate the value of each to 4 decimal places: i)sin 43sin 137sin 223sin 317. ii) cos 25cos 155cos 205cos 335. iii)tan 71tan 109 tan 251tan 289.

A. Calculate the value of each to 4 decimal places: i)sin 43sin 137sin 223sin 317. ii) cos 25cos 155cos 205cos 335. iii)tan 71tan 109 tan 251tan 289.

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