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Valentin [98]
3 years ago
8

Anyone know how to do trig? Given tan Ф = 4/5, find all other trig functions.

Mathematics
1 answer:
mars1129 [50]3 years ago
7 0

9514 1404 393

Answer:

  • sin(Ф) = (4/41)√41; csc(Ф) = (√41)/4
  • cos(Ф) = (5/41)√41; sec(Ф) = (√41)/5
  • tan(Ф) = 4/5; cot(Ф) = 5/4

Step-by-step explanation:

The mnemonic SOH CAH TOA can help you with three of the functions. Then you need to remember the relations between those and the other three.

  Tan = Opposite/Adjacent

  tan(Ф) = 4/5

This suggests you can draw a triangle like the one attached that has adjacent side 5 and opposite side 4. Then hypotenuse can be found from the Pythagorean theorem:

  AC² = AB² +BC² = 5² +4² = 41

  AC = √41 . . . . . hypotenuse

Then the other trig functions are ...

  Sin = Opposite/Hypotenuse

  sin(Ф) = 4/√41 = (4/41)√41

  Cos = Adjacent/Hypotenuse

  cos(Ф) = 5/√41 = (5/41)√41

And the reciprocal functions are ...

  csc(Ф) = 1/sin(Ф) = (√41)/4

  sec(Ф) = 1/cos(Ф) = (√41)/5

  cot(Ф) = 1/tan(Ф) = 5/4

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Roots of Quadratics 50 PTS!!!
noname [10]

The values of k for the different quadratic equation solutions are as follows

a  the equation 2x² - x + 3k = 0 has two distinct real roots

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b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots

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ci the equation -x² + 3x + (k + 1) = 0 has real roots

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Quadratic equations of the form ax² + bx + c = 0 is solved using the formula

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The equation b² - 4ac is called the discriminant and it is used as follows

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substituting the values gives

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divide through by coefficient of k

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To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0

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substituting the values gives

(-2)² - 4 * 5 * (2k - 1) = 0

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divide through by coefficient of k

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substituting the values gives  

(3)² - 4 * -1 * (k+1) > 0

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divide through by coefficient of k

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To solve the equation and get  no real solutions  3kx² - 3x + 2 = 0

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substituting the values gives  

(-3)² - 4 * 3k * 2 < 0

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divide through by coefficient of k²

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Learn more about roots of quadratic equations: brainly.com/question/26926523

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