Mia M.

asked • 02/24/20

Can someone answer these trig questions

Find the values of the 6 trig functions of theta if cos2theta=7/24 and 270 degrees< theta< 360 degrees


given costheta= 3/7 and sintheta<0, find sin2theta, cos2theta, tan2theta

Mark M.

If cos^2 theta = 7/24, then cos theta cannot be equal to 3/7. Check your data.
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02/24/20

Edward A.

Mark, I think he’s giving us two separate problems. Actually, I question that 7/24 is cos^2. These problems tend to have rational sides, so I would expect cot(theta) = 7/24, so that the hypotenuse could be 25.
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02/24/20

Mark M.

Edward, agreed. Students must know how to pose questions correctly if a correct response is expected. On occasion that can lead to the student answering.
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02/24/20

1 Expert Answer

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Sidney P. answered • 02/24/20

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In the first problem, given that we are in 4th quadrant, let adj side = √7 and hypotenuse = √24. Using Pythagorean Theorem, opp = -√17. So sin θ = -√17 / √24; cos θ = √7 / √24; tan θ = -√17 / √7; csc θ = -√24 / √17; sec θ = √24 / √7; cot θ = -√7 / √17. (I'm not taking the time to normalize these to get rid of radicals in denominators, which your teacher may prefer).


Second problem is also 4th quadrant according to the constraints. P.T. yields opposite side = -√40. Sin2 θ = 40/49; cos2 θ = 9/49; tan2 θ = 40/9.

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