How do you use double-angle identities to find the exact value of sin 2x & cos 2x when csc(x) = -25/7 and cos x>0?

1 Answer
Apr 23, 2018

Find sinx first and then find sin2x and cos2x.

Explanation:

As cosx > 0, the basic angle must be in quadrant II or III.
As cscx = 257, the basic angle must be in quadrant III as cscx = 1sinx.

By algebra, sinx = 725. From there, you can draw the triangle and find out what the basic angle is.
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sin2x = 2sinxcosx
cos2x = 12sin2x (there are other variations but this works better for this question)

From the triangle, we can find that cosx=2425
The negative sign is because the basic angle is in the third quadrant, where only tangent is positive,

Evaluating sin2x and cos2x, sin2x = 336625 and cos2x = 527625.

The negative signs are because the angles fall in the third quadrant. Not so sure about that though.