Pre-Calculus Take-home Quiz



Pre-Calculus Quiz Review

Sections 5.1 & 5.2

Please work through each problem. Show your work and write your answer in the blank.

Given the following points on the terminal side of θ, find the value of cos θ and sin θ.

|1. (4, -4) |2. (-¾, 2) |

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|cos θ = ________ sin θ = _________ |cos θ = ________ sin θ = _________ |

|3. If cos θ = ½, find the point(s) where the terminal side(s) of θ intersects the unit circle. Also, find the reference angle, θ′ and the value(s) |

|of θ for 0 < θ < 2π. |

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|θ′ = __________ θ = _________ and ________ Points: ___________ and ____________ |

|4. a) Convert to DMS: 61.24° |

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|b)Convert to decimal degrees: 98°22’45” |

|5. Given the angle [pic], find the reference angle, θ′, and two co-terminal angles, one positive and one negative. |

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|θ′ = __________ Positive Co-terminal angle:_________ Negative Co-terminal angle:__________ |

6. Change the following angles to degrees. Show your work!

|a) [pic] |b) [pic] |c) [pic] |d) [pic] |

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|a)________ |b)_________ |c)_________ |d)_________ |

7. Change the following angles to radians.

|a) 240° |b) 135° |c) 540° |d) -270° |

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|a)________ |b)________ |c)________ |d)________ |

Please find the exact values for the six trig functions given the following information. Leave your answers as fractions in reduced radical form.

|8. The point (12, -5) is on the terminal side of θ. |9. [pic]is a point on the unit circle. |

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| |sin θ = ______ cos θ = ______ tan θ = ______ |

|sin θ = ______ cos θ = ______ tan θ = ______ | |

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| |csc θ = ______ sec θ = ______ cot θ = ______ |

|csc θ = ______ sec θ = ______ cot θ = ______ | |

|10. [pic] |11. sin θ = [pic], and tan θ > 0. |

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| |sin θ = ______ cos θ = ______ tan θ = ______ |

|sin θ = ______ cos θ = ______ tan θ = ______ | |

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| |csc θ = ______ sec θ = ______ cot θ = ______ |

|csc θ = ______ sec θ = ______ cot θ = ______ | |

|12. Use a calculator to evaluate cos 20 |13. Use a calculator to evaluate sin 20° |

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|12)_________________________ |13)_________________________ |

|14. If tan θ = 6.1234, in which quadrants could θ lie for 0°≤θ≤360°? |15. If the radius of a circle is 2 inches and it has a central angle of |

| |70°, what is the length of the arc that is subtended by the angle? |

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|14)__________ AND ______________ |15)_________________________ |

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