What is the value of sin ((5 π/12)) ?

Question

What is the value of sin ((5 π/12)) ? (A) (√3+1/2) (B) (√6+√2/4) (C) (√3+√2/4) (D) (√6+1/2)

Tardigrade Admin · Accepted Answer

sin (5 π/12)= sin 75° = sin (45°+30°)= sin 45° cos 30°+ cos 45° sin 35° =(1/√2) ⋅ (√3/2)+(1/√2) ⋅ (1/2)=(1/√2)((√3+1/2)) =(√3+1/2 √2) × (√2/√2)=(√6+√2/4)

Q. What is the value of $sin (\frac{5 π}{12}) ?$

$\frac{3 + 1}{2}$

$\frac{6 + 2}{4}$

$\frac{3 + 2}{4}$

$\frac{6 + 1}{2}$

$sin \frac{5 π}{12} = sin 7 5^{\circ}$
$= sin (4 5^{\circ} + 3 0^{\circ}) = sin 4 5^{\circ} cos 3 0^{\circ} + cos 4 5^{\circ} sin 3 5^{\circ}$
$= \frac{1}{2} \cdot \frac{3}{2} + \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{2} (\frac{3 + 1}{2})$
$= \frac{3 + 1}{2 2} \times \frac{2}{2} = \frac{6 + 2}{4}$

Q. What is the value of sin(125π​)?

23​+1​

46​+2​​

43​+2​​

26​+1​

sin125π​=sin75∘ =sin(45∘+30∘)=sin45∘cos30∘+cos45∘sin35∘ =2​1​⋅23​​+2​1​⋅21​=2​1​(23​+1​) =22​3​+1​×2​2​​=46​+2​​

Q. What is the value of $sin (\frac{5 π}{12}) ?$

$\frac{3 + 1}{2}$

$\frac{6 + 2}{4}$

$\frac{3 + 2}{4}$

$\frac{6 + 1}{2}$