Question

Find sin(x/2), cos(x/2), and tan(x/2) from the given information.

Answer 1

The values of sin (x/2) = 4/√17,   cos (x/2) = 1/√17 and  tan (x/2) = 4.

What is Trigonometry?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

Here, cos x = -15/17  (given)

we know, cos x = 2cos²x/2 - 1

                cos²(x/2) = (cos x + 1)/2

                  cos²(x/2) = (-15/17 + 1)/2

                 cos²(x/2) = 1/17

                 cos (x/2) = 1/√17

then, sin (x/2) = √(1- cos²(x/2))  

          sin (x/2) = √(1 - 1/17)

          sin (x/2) = √16/17

          sin (x/2) = 4/√17

and tan (x/2) = sin (x/2) / cos (x/2)  

       tan (x/2) = $\frac{4/\sqrt{17} }{1/\sqrt{17} }$

       tan (x/2) = 4

Thus, the values of sin (x/2) = 4/√17,   cos (x/2) = 1/√17 and  tan (x/2) = 4.

Learn more about Trigonometry from:

brainly.com/question/22698523

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