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find the exact values of sin (u/2), cos (u/2), and tan (u/2) using the half - angle formulas.

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(a) Determine the quadrant in which u/2 lies, and (b) find the exact values of sin (u/2), cos (u/2), and tan (u/2) using the half - angle formulas.

cos u = 7/25,       0 < u < π/2
asked Jan 22, 2015 in TRIGONOMETRY by anonymous

1 Answer

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Step 1:

(a)

The trigonometric function is image, image.

Since image lies in quadrant I, then image is also lies in quadrant I.

Step 2:

(b)

Find image.

Using half - angles formulas : image.

Substitute image in above formula.

image

image.

Step 3:

Find image.

Using half - angles formulas : image.

Substitute image in above formula.

image

image.

Step 4:

Find image.

Using half - angles formulas : image.

From Pythagorean theorem, image.

Substitute image and image in above formula.

image

image.

Solution :

(a) image lies in quadrant I.

(b) image, image and image.

answered Jan 23, 2015 by joseph Apprentice

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