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Math Help - 3 functions

  1. #1
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    3 functions

    Three functions are defined as follows:

    f: x ---> cos x for the domain 0 <= x <= 180
    g: x ---> sin x for the domain 0 <= x <= 90
    h: x ---> tan x for the domain p <= x <= q

    1) find the range of f

    Is the answer: It ranges from cos (0) = 1 to cos (180) = -0.9510565163

    2) Given that the range of h is the same as the range of g. Find the value of p and q.

    Is the answer: p = 0 as tan (0) = 0 and q = not sure??
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  2. #2
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    Cosine goes from -1 to 1 cos(180)=-1

    tan(90)=DNE tan(z)=y/x when the angle is 90 y=1 and x=0; therefore, 1/0 is undefined. tan isn't less than or equal to 90 but simply less than.

    The range of tangent is -90<x<90 excluding the end values.
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  3. #3
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    Quote Originally Posted by Natasha1 View Post
    Three functions are defined as follows:

    f: x ---> cos x for the domain 0 <= x <= 180
    g: x ---> sin x for the domain 0 <= x <= 90
    h: x ---> tan x for the domain p <= x <= q

    1) find the range of f

    Is the answer: It ranges from cos (0) = 1 to cos (180) = -0.9510565163
    How in the world did you get that? Actually, I would have to say the whole problem is badly phrased. The function "f:x--->cos x", as opposed to a problem where we are actually dealing with angles measured in degrees, requires that x be in radians. At first I thought that was what you are doing but the cosine of 180 radians is -0.59846, not what you give. Oh wait! Cosine of 180 grads is -0.9510565. But why in the world would your calculator be set to "grads"? (There are 100 grads in a right angle.)

    2) Given that the range of h is the same as the range of g. Find the value of p and q.
    For x between 0 and 90 degrees (which should have been said explicitely) sine is between 0 and 1. Yes, tan(0)= 0. What angle, x, has tan(x)= 1?

    Is the answer: p = 0 as tan (0) = 0 and q = not sure??
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