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Math Help - Sketch a triangle that has acute angle θ, and find the other five trigonometric ratio

  1. #1
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    Sketch a triangle that has acute angle θ, and find the other five trigonometric ratio

    My book provides an example how to do cos alpha 3/4. I know how to do cos. But there are no examples for tangent. I'm sure pythagoras theorem will be used but i do not understand where the 4 is coming from.
    Sketch a triangle that has acute angle θ, and find the other five trigonometric ratio-trig-ratio.png
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  2. #2
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    If the cosine of the angle is 3/4, draw a right-angled triangle with sides 3, \sqrt{7} and hypotenuse 4. This satisfies the Pythagorean Theorem. The 4 is given in the problem, \sqrt{7} is the calculated value for the side that is not given. Now the tangent would be (opposite side/adjacent side) = \sqrt{7}/3. The sine would be the opposite side divided by the hypotenuse.

    Is this what you are asking?
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  3. #3
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    no, i would like to see how one goes about solving what i attached, the tangent theta = square root 15. i do not know where the four comes from. also, if a formula could be provided for how one solves the problem i attached. i only mentioned cosine 3/4 to show i understand how to do these types of problems regarding cosines.
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  4. #4
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    i figured it out
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