The exact values for the sine, cosine and tangent of the half angle are listed below:
- sin 0.5x = 0.998
- cos 0.5x = 0.062
- tan 0.5x = 16.097
<h3>How to find the exact values of half angle formulas</h3>
In this problem we find the exact value of cosecant of an angle in the second quadrant and we are supposed to find the exact values of the sine, the cosine and the tangent of an half angle. The required expressions are listed below:
csc x = 1 / sin x = √(x² + y²) / y
sin x = y / √(x² + y²)
cos x = x / √(x² + y²)
sin 0.5x = √[(1 - cos x) / 2]
cos 0.5x = √[(1 + cos x) / 2]
tan 0.5x = sin 0.5x / cos 0.5x
First, determine the components associated to the cosecant function:
x < 0, y > 0
y = 1
x = - 3√7
Second, calculate the values of the sine and the cosine of the angle:
sin x = 1 / 8
cos x = - 3√7 / 8
Third, determine the exact values of the half angle formulas:
sin 0.5x > 0
sin 0.5x = √[(1 + 3√7 / 8) / 2]
sin 0.5x = 0.998
cos 0.5x > 0
cos 0.5x = √[(1 - 3√7 / 8) / 2]
cos 0.5x = 0.062
tan 0.5x > 0
tan 0.5x = sin 0.5x / cos 0.5x
tan 0.5x = 0.998 / 0.062
tan 0.5x = 16.097
To learn more on trigonometric equations: brainly.com/question/22624805
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