-1-√2
Sine, Cosine or Tangent (are also called sin, cos and tan) they are each a ratio of sides of a right angled triangle:. For a given angle θ every ratio stays the same no matter how big and small the triangle is. To calculate it just Divide the length of one side by another side.
You need to apply the "Half-angle identity for tangent", which is:
Tan(θ/2)=Sinθ/1+Cosθ
But first, the angle 5π/4 must be expressed as a product of 1/2, as below:
5π/8=(5π/4)(1/2)
Now, you can substitute the angle to 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
now,
=(-√2/2)/(1-√2/2)
When you simplify the expression, you obtain:
=-1-√2
Therefore, the answer is: -1-√2
What is the formula for sin cos and Tan?
The sin cos and tan formulas are:
- sin A = Opposite side/Hypotenuse
- cos A = Adjacent side/Hypotenuse
- tan A = Opposite side/Adjacent side
Learn more about sin cos and tan here https://brainly.com/question/1619932
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