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Mathematics
Kaeden
21 July, 16:31
Tan 5pi/8 exact value
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Valeria Hess
21 July, 19:06
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To solve this exercirse, you must apply the proccedure below:
1. You need to apply the "Half-angle identity for tangent", which is:
Tan (θ/2) = Sinθ/1+Cos θ
2. But first, the angle 5 π/4 must be expressed as a product of 1/2, as below:
5π/8 = (5π/4) (1/2)
3. Now, you can susbtitute the angle into the formula:
=Sinθ/1+Cosθ
=Sin (5π/4) / 1+Cos (5π/4)
Sin (5π/4) = - √2/2
Cos (5π/4) = Cos (π/4)
π/4 is the reference angle of 5π/4
π/4=√2/2
4. Then:
= (-√2/2) / (1-√2/2)
5. When you simplify the expression, you obtain:
=-1-√2
6. Therefore, the answer is: - 1-√2
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