Jordan R.

asked • 11/29/16

If cosθ = 20/29 and 0 < θ < π/2 then what is the value for tanθ

A> A. 21/29
B. 21/20
C. 20/21
D. 29/21

Additional Question: 
For 0° ≤ x ≤ 360° and sinx =0.631 then what is the approximate values of x?
A.{0.590, 179.410}
B. {0.011, 179.989}
C. {39.124, 219.123}
D. {39.124, 140.876}

Kenneth S.

Additional Question:
For 0° ≤ x ≤ 360° and sinx =0.631 then what are the approximate values of x?
A.{0.590, 179.410}
B. {0.011, 179.989}
C. {39.124, 219.123}
D. {39.124, 140.876}
using inverse sine function, x = 39.124o or, of course, 180o - 39.124o 
 
You can convert these to radians, or do the inverse sine operation whilst your calculator is in RADIAN mode.
To get the second answer, subtract the first answer you get from pi.
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11/29/16

1 Expert Answer

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Kenneth S. answered • 11/29/16

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Theta is in the first quadrant and can be shown to relate to a right triangle with horizontal leg 20, hypotenuse 29.
Using Pythagorean Theorem (or Pythagorean identity), the other leg of triangle is 21, i.e. sine = 21/29.
Therefore tan of theta = 21/20.
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