Using half-angle identities

[AlexDoesMath]

Given: tan x -24/7 and x is in Quadrant IV.
Find exact values of sin(x/2), cos(x/2), and tan(x/2). 0 is less than or equal to x and x is less than ir equal to 360 degrees. Don’t need to solve for x.

 

[JeffM]

Is that [MATH]tan(x) = - \dfrac{24}{7}[/MATH] or [MATH]tan(x) - \dfrac{24}{7}[/MATH]?

In the latter case are you told what the difference equals?

 

[Otis]

… [angle] x is in Quadrant IV … 0 [degrees] is less than or equal to x and x is less than or equal to 360 degrees …

Hi Alex. Let's recall that neither the x-axis nor the y-axis belong to any Quadrant. Therefore, a Quadrant IV angle (i.e., an angle whose terminal ray lies in Quadrant IV) cannot be either 0º or 360º because each of those angles would have their terminal ray on top of the x-axis (hence, not in a quadrant). The given inequalities need to be corrected, so that x is a Quadrant IV angle:

270º < x < 360º

Assuming that you meant to type tan(x) = -24/7, you'll find the following identities helpful. (I've assumed that you have a listing of basic trigonometric identities to look at.)

tan(x) = sin(x)/cos(x)

the half-angle identities for tangent, sine, and cosine

Please show us how far you get trying to find sin(x/2). We can help from there. If you're still not sure how to begin, let us know.

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