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anonymous

  • one year ago

The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

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  1. anonymous
    • one year ago
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    please help anyone

  2. anonymous
    • one year ago
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    @pooja195

  3. anonymous
    • one year ago
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    @phi

  4. Zale101
    • one year ago
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    |dw:1438125246483:dw|

  5. Zale101
    • one year ago
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    |dw:1438125391747:dw|

  6. anonymous
    • one year ago
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    |dw:1438125791505:dw|

  7. Zale101
    • one year ago
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    You first, find all the sides, and use trig identities to determine what cosine, sine, and tangent are. \(cos(\theta)=\Large \frac{Adjacent}{Hypotenuse}\) \(sin(\theta)=\Large \frac{Opposite}{Hypotenuse}\) \(tan(\theta)=\Large \frac{Opposite}{adjacent }\)

  8. Zale101
    • one year ago
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    |dw:1438125668700:dw|

  9. anonymous
    • one year ago
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    the degree

  10. Zale101
    • one year ago
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    I used the Pythagorean theorem to find r, since we already have x and y given (2,3)

  11. Zale101
    • one year ago
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    how did you find the degree?

  12. anonymous
    • one year ago
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    using the unit circle

  13. Zale101
    • one year ago
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    The unit circle shifts 1 unit across and 1 unit upward and downward. There's no point (2,3) on the unit circle.

  14. Zale101
    • one year ago
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    However, there's degrees and radians which applies to all circle.

  15. Zale101
    • one year ago
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    circles*

  16. Zale101
    • one year ago
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    You are given a point. You find all the sides of the triangle. Use trig identities and then inverse to solve for the angle. Your goal is to find angle theta and that is the steps to find it.

  17. Zale101
    • one year ago
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    I'm still confused on how you got theta straight from looking at the unit circle.

  18. anonymous
    • one year ago
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    because i know in the unit circle pi/4 is in the middle and that is 45 degrees and because point (2,3) looks like its in the middle i had just assume that it would be 45 degrees

  19. Zale101
    • one year ago
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    Although the correct degree is closer to 45, 45 degrees is incorrect. Therefore, your assumption is wrong. If the point was (2,2), then theta is 45 degrees. We don't assume the answers with trig, we do math just like how we do math to solve for x in algebra but slightly different. Math is math. We do math to solve for math problems.

  20. Zale101
    • one year ago
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    Here are the steps to your problem when finding the terminal side of angle θ by a given point Step 1: Label the given point on the graph Step 2: Draw a right triangle and label the sides. X, y, and r (like i did above) Step 3: Label the adjacent and opposite sides. (x, y) x is the adjacent, y is the opposite sides Step 4: Use the Pythagorean theorem to solve for the hypotenuse (r) Step 5: Use trig identities for sine, cosine, and tangent. Ex. Cosine is adj/hyp.

  21. anonymous
    • one year ago
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    the hypotenuse would be |dw:1438127320268:dw|

  22. Zale101
    • one year ago
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    |dw:1438127050766:dw|

  23. Zale101
    • one year ago
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    I'm sure you have completed all the four steps i gave above. Now, you are in the fifth step .

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