Question

sin 45sin 30 cos 45 cos 30

Answer 1

Answer:

$\large\boxed{\frac{\sqrt{3} }{8}=0.21650 }$

Step-by-step explanation:

To solve this problem, first you have to trivial identify of sin and cos.

Given:

sin(45°) sin(30°) cos(45°) cos(30°)

Solutions:

First, you have to trivial identify of sin.

$\displaystyle \sin(45)^{\circ}=\frac{\sqrt{2} }{2}$

$\displaystyle \sin(30)^{\circ}=\frac{1}{2}$

Next, trivial identify of cos.

$\displaystyle \cos(45)^{\circ}=\frac{\sqrt{2} }{2}$

$\displaystyle cos(30)^{\circ}=\frac{\sqrt{3} }{2}$

Then, multiply fractions from left to right.

$\displaystyle \frac{\sqrt{2}  }{2}*\frac{1}{2}*\frac{\sqrt{2} }{2}*\frac{\sqrt{3} }{2}$

$\large\boxed{\textnormal{Radical Rule}}$

$\displaystyle \sqrt{b} \sqrt{b}=b$

$\displaystyle \sqrt{2}  \sqrt{2}=2*1=2$

Multiply numbers from left to right.

$\displaystyle 1*2=2$

$\displaystyle 2\sqrt{3}$

Rewrite the problem down.

$\displaystyle \frac{2\sqrt{3} }{2*2*2*2}$

Multiply.

$\displaystyle 4^2=16, 2*2*2*2=16$

$\displaystyle \frac{2\sqrt{3} }{16}$

Common factor of 2.

Make sure to divide numbers from left to right.

$\displaystyle 16\div2=8$

$\large\boxed{\frac{\sqrt{3} }{8} }$

As a result, the final answer is √3/8=0.21650.