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anonymous

  • one year ago

PRE-CALCULUS: Find the exact value of cos-1 the quantity square root of three divided by two.

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  1. anonymous
    • one year ago
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    \[\cos^{-1} \left( \frac{ \sqrt{3} }{ 2} \right)\]

  2. anonymous
    • one year ago
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    we know that the range arccos(x) is 0 ≤ x ≤ π/2 ==> 0° ≤ x ≤ 180°. So we need to find the solution to cos(x) = -√3/2 this in the range of [0°, 180°]. If we construct a 30-60-90 triangle, we see that the 30° angle corresponds to this and so the angle required is x = 180° - 30° = 150°. Thus, arccos(-√3/2) = 150° = 5π/6. Answer provided by Yahoo Answers :)

  3. anonymous
    • one year ago
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    The answer amber provided was for \[\sf \large-\frac{\sqrt{3}}{2}\] by the way

  4. anonymous
    • one year ago
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    I think your answer is wrong, but the way you explain it is right.

  5. anonymous
    • one year ago
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    I know @LegendarySadist :)

  6. anonymous
    • one year ago
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    The easiest way to go about this sort of problem is simply to utilize the unit circle.

  7. anonymous
    • one year ago
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    For cos, the range is 0<y<pi, right?

  8. anonymous
    • one year ago
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    Yes, I actually based my answer on the unit circle. My answer is \[\frac{ \pi }{ 6 }\]

  9. campbell_st
    • one year ago
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    here is a triangle |dw:1437262431290:dw| so the cosine of which angle is \[\cos(?) = \frac{\sqrt{3}}{2}\]

  10. anonymous
    • one year ago
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    It is 30 degrees.

  11. anonymous
    • one year ago
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    right @campbell_st ?

  12. campbell_st
    • one year ago
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    that's correct...

  13. campbell_st
    • one year ago
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    you just need to remember the exact value triangles... I always think about the longest side is opposite the largest angle 2 = 90 1 = 30 shortest and smallest angle

  14. anonymous
    • one year ago
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    @campbell_st Oh, I don't that one. It is Geometry. Thanks for the help! :)

  15. campbell_st
    • one year ago
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    it is a property from geometry that can be applied to any triangle.. so its handy to know for trig... seeing trig is about triangle measurements

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