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JayDelV

  • one year ago

Sine, Cosine, and Tangent of 45 degrees?

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  1. UnkleRhaukus
    • one year ago
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    |dw:1439360650195:dw|

  2. UnkleRhaukus
    • one year ago
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    |dw:1439360684499:dw|

  3. UnkleRhaukus
    • one year ago
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    we need to set the lengths of the sides of the triangle for simplicity we can set the adjacent side to be 1

  4. UnkleRhaukus
    • one year ago
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    what will the other sides of the triangle be if the adjacent side is 1?

  5. JayDelV
    • one year ago
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    Wait what do you mean?

  6. JayDelV
    • one year ago
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    This is actually a timed test and I'm super tired

  7. UnkleRhaukus
    • one year ago
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    |dw:1439361178381:dw|

  8. UnkleRhaukus
    • one year ago
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    (notice it is an isosceles triangle )

  9. JayDelV
    • one year ago
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    I forgot how to do this and I don't have a calculator with me. Is there another way?

  10. UnkleRhaukus
    • one year ago
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    this way doesn't need a calculator

  11. UnkleRhaukus
    • one year ago
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    [isosceles triangle have a pair of sides of equal length]

  12. UnkleRhaukus
    • one year ago
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    [the sides of equal length, will be opposite to the angles of equal measure]

  13. JayDelV
    • one year ago
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    Ohhhhhhh so 1

  14. UnkleRhaukus
    • one year ago
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    yes

  15. UnkleRhaukus
    • one year ago
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    |dw:1439361833342:dw|

  16. UnkleRhaukus
    • one year ago
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    now \[\tan\theta = \frac{\text{opp}}{\text{adj}}\]

  17. UnkleRhaukus
    • one year ago
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    so tan 45° = / =

  18. UnkleRhaukus
    • one year ago
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    What do you get?

  19. JayDelV
    • one year ago
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    so confused but 1/ over something, I'm not sure what the hypotenuse is

  20. UnkleRhaukus
    • one year ago
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    we don't need the hypotenuse for tan (we will need it for sine and cosine)

  21. JayDelV
    • one year ago
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    oh opposite adjacent

  22. JayDelV
    • one year ago
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    sorry

  23. JayDelV
    • one year ago
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    1/1

  24. UnkleRhaukus
    • one year ago
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    Great! which simplifies to 1 So we have tan 45° = 1

  25. UnkleRhaukus
    • one year ago
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    now we need to work out the length of that hypotenuse. we have a right angled triangle, so we can use Pythagorus a^2 + b^2 = c^2 where a and b are the adj and opp, and c is the hypo

  26. UnkleRhaukus
    • one year ago
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    so hypo = √( adj^2 + opp^2 )

  27. UnkleRhaukus
    • one year ago
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    plug in adj = 1, opp = 1

  28. UsukiDoll
    • one year ago
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    that's one of the standard triangles. |dw:1439362733572:dw|

  29. UnkleRhaukus
    • one year ago
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    why remember, when you can work it out

  30. UsukiDoll
    • one year ago
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    \[\tan 45 = 1 , \sin 45 = \frac{1}{\sqrt{2}}, \cos 45 = \frac{1}{\sqrt{2}} \]

  31. UnkleRhaukus
    • one year ago
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    why bother to learn pythag. and triangle geometry ?

  32. JayDelV
    • one year ago
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    Thank you both :)

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