U6D2 Radians and Reference Angles Apr22

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Explain why the equation cos(A) = sin(C) is valid.

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Given the measure of angle A is 30 degrees, find the sine, cosine and tangent values of angle A. Round your answers to the nearest thousandths. If you are getting weird answers, then you may need to change your calculator settings to "degrees."
sin 30 = _______ 
cos 30 = _______ 
tan 30 = _______   

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Draw a square.
Draw one diagonal for your square. The length of your diagonal is 1 unit.
Label the measure of all the angles in your square.
Don't forget the angles around the diagonals.

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Use the Pythagorean Theorem or the properties of special right triangles to determine the lengths of the legs of the triangle. (Leave your answers in simplest radical form.) Label the endpoint of the 45° line with an ordered pair using the values that you found for the legs of the triangle. Draw triangles for all the lines with a reference angle of 45° and determine the ordered pairs for the end of each line.

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Draw an equilateral triangle with each side equal to 1 unit.
Construct a perpendicular bisector for the equilateral triangle. This cuts the triangle in half. Label the measure of all the angles around your drawing.

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Use the Pythagorean Theorem or the properties of special right triangles to determine the lengths of the legs of the triangle. (Leave your answers in simplest radical form.) Label the endpoint of the 30° line with an ordered pair using the values that you found for the legs of the triangle. Draw triangles for all the lines with a reference angle of 30° and determine the ordered pairs for the end of each line.

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Use special right triangles to determine the exact (x, y) coordinates where each angle with a 60o reference angle intersects the unit circle. Draw each angle on the unit circle and clearly label the coordinates. Record your answers in the table.

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Think about what happens as you get to angles greater than 360o.
How can you predict the value of the sin of 420o?

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What about the cosine of 600o?

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Does the same thing happen for negative angles?

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Using your understanding of the unit circle and
to complete the chart below for the indicated angles.

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What will happen for the tangent value if you change the angle to 0°?

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What will happen for the tangent value if you change the angle to 90°?

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150o written in radians is _______ 

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45o written in radians is _______ 

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converted to degrees would be _______ 

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converted to degrees would be _______ 

Explain why the equation cos(A) = sin(C) is valid.

Draw a square. Draw one diagonal for your square. The length of your diagonal is 1 unit. Label the measure of all the angles in your square. Don't forget the angles around the diagonals.

Draw an equilateral triangle with each side equal to 1 unit. Construct a perpendicular bisector for the equilateral triangle. This cuts the triangle in half. Label the measure of all the angles around your drawing.

Use special right triangles to determine the exact (x, y) coordinates where each angle with a 60o reference angle intersects the unit circle. Draw each angle on the unit circle and clearly label the coordinates. Record your answers in the table.

Think about what happens as you get to angles greater than 360o. How can you predict the value of the sin of 420o?

What about the cosine of 600o?

Does the same thing happen for negative angles?

Using your understanding of the unit circle andto complete the chart below for the indicated angles.

What will happen for the tangent value if you change the angle to 0°?

What will happen for the tangent value if you change the angle to 90°?

Draw a square.
Draw one diagonal for your square. The length of your diagonal is 1 unit.
Label the measure of all the angles in your square.
Don't forget the angles around the diagonals.

Draw an equilateral triangle with each side equal to 1 unit.
Construct a perpendicular bisector for the equilateral triangle. This cuts the triangle in half. Label the measure of all the angles around your drawing.

Think about what happens as you get to angles greater than 360o.
How can you predict the value of the sin of 420o?

Using your understanding of the unit circle and
to complete the chart below for the indicated angles.