MATH SOLVE

7 months ago

Q:
# tan 5pi/8 exact value

Accepted Solution

A:

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+Cosθ

2. But first, the angle 5π/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

1. You need to apply the "Half-angle identity for tangent", which is:

Tan(θ/2)=Sinθ/1+Cosθ

2. But first, the angle 5π/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