Exam 1: The Six Trigonometric Functions

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Graph the circle Graph the circle   with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate.   ​ with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Graph the circle   with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate.   ​ ​

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Suppose ABC  is a right triangle with C = 90°. If a = 6 and b = 8, find c .

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If csc θ = 5 and cos  θ    is negative, find  cot  θ . ​

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Find the remaining trigonometric functions of θ  if Find the remaining trigonometric functions of θ  if    and θ  terminates in QII. ​  and θ  terminates in QII. ​

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Find β  if B = 4 β . Find β  if B = 4 β .   Remember: The sum of the three angles in any triangle is always 180°. Remember: The sum of the three angles in any triangle is always 180°.

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Solve for x . Solve for x .     , b = 1 ​ Solve for x .     , b = 1 ​ , b = 1 ​

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Give the complement and the supplement of angle  z .  ​

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Solve for x . Solve for x .   a = 5,    ​ a = 5,  Solve for x .   a = 5,    ​ ​

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Find y if the point (8, y )is on the terminal side of θ  and Find y if the point (8, y )is on the terminal side of θ  and

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Multiply. Multiply.

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A searchlight rotates through one complete revolution every 2 seconds. How long does it take the light to rotate through 180°? __________ sec.

(Short Answer)
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Find all six trigonometric functions of θ  if the given point is on the terminal side of θ . Find all six trigonometric functions of θ  if the given point is on the terminal side of θ .   ​ ​

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If If    and   , find tan θ . ​  and If    and   , find tan θ . ​ , find tan θ . ​

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If If    and θ  is not in QII, find tan  θ . ​  and θ  is not in QII, find tan  θ . ​

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Show that the following statement is true by transforming the left side into the right side. Show that the following statement is true by transforming the left side into the right side.

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Find x so the distance between Find x so the distance between   and   is   x = __________ and Find x so the distance between   and   is   x = __________ is Find x so the distance between   and   is   x = __________ x = __________

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Use your calculator to find sin  θ  and cos  θ  if the point Use your calculator to find sin  θ  and cos  θ  if the point   is on the terminal side of  θ .  sin θ = __________  cos θ = __________ is on the terminal side of  θ . sin θ = __________ cos θ = __________

(Short Answer)
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Graph the parabola. Graph the parabola.   ​ ​

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