Question 908869: if tangent of theta equals 5 divided by 7, then cosine of theta will equal ?
These types of question on my homework give you tangent or one of the other trig ratios and ask what cosine or one of the other trig ratios will be.
I know what each trig function means sine is opposite over hypotenuse and so forth but i cant figure out how to go about solving this problem. Since tangent is opposite over adjacent I need to figure out the hypotenuse to know what cosine of theta is. Please help me I have a test tomorrow and i have forgotten how to do these types of questions.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! if tangent of theta equals 5 divided by 7, then cosine of theta will equal ?
These types of question on my homework give you tangent or one of the other trig ratios and ask what cosine or one of the other trig ratios will be.
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Procedure::
Any given trig function value will tell two of the three values
you need to know:: x, y, and r.
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In your problem tan(t) = 5/7 tell you y = 5 and x = 7
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x, y, and r are related by the Pythagorean formula :: r^2 = x^2 + y^2
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In you case r = sqrt(5^2+7^2) = sqrt(74)
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Assuming that t in in the 1st quadrant you have::
sin = y/r = 5/sqrt(74)
cos = x/r = 7/sqrt(74)
tan = y/x = 5/7
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csc = r/y
sec = r/x
cot = x/y
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The sign values depend on which Quadrant the angle is in.
Cheers,
Stan H.
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