Question

Sin п/12+ cos п/12 вычислите

Answer 1

$sin\frac{\pi }{12}+cos\frac{\pi }{12}=\sqrt2\cdot (\frac{1}{\sqrt2}\cdot sin\frac{\pi }{12}+\frac{1}{\sqrt2}\cdot cos\frac{\pi }{12})=\Big [\frac{1}{\sqrt2}=\frac{\sqrt2}{2}=cos\frac{\pi}{4}=sin\frac{\pi}{4}\Big ]=\\\\=\sqrt2\cdot (cos\frac{\pi }{4}\cdot sin\frac{\pi }{12}+sin\frac{\pi }{4}\cdot cos\frac{\pi }{12})=\sqrt2\cdot sin(\frac{\pi}{4}+\frac{\pi}{12})=\\\\=\sqrt2\cdot sin\frac{4\pi }{12}=\sqrt2\cdot sin\frac{\pi}{3}=\sqrt2\cdot \frac{\sqrt3}{2}=\frac{\sqrt6}{2}\; \; \Big (=\sqrt{\frac{3}{2}}\, \Big )$

$\star \; \; sin\alpha \cdot cos\beta +sin\beta \cdot cos\alpha =sin(\alpha +\beta )\; \; \star$

Answer 2

To calculate the value of the expression sin(π/12) + cos(π/12), you need to know the values of sine and cosine for the angle π/12. Let's calculate it step by step:

Step 1: Find the value of sin(π/12). Step 2: Find the value of cos(π/12). Step 3: Add the results from Step 1 and Step 2.

Step 1: Find the value of sin(π/12). Using a calculator or a trigonometric table, sin(π/12) is approximately 0.2588190451.

Step 2: Find the value of cos(π/12). Using the identity cos(θ) = sin(π/2 - θ), we can find cos(π/12) as follows: cos(π/12) = sin(π/2 - π/12) = sin(5π/12).

Step 2.1: Find the value of sin(5π/12). Using a calculator or a trigonometric table, sin(5π/12) is approximately 0.9659258263.

Step 2.2: Find the value of cos(π/12). cos(π/12) = sin(5π/12) ≈ 0.9659258263.

Step 3: Add the results from Step 1 and Step 2. sin(π/12) + cos(π/12) ≈ 0.2588190451 + 0.9659258263 ≈ 1.2247448714.

So, sin(π/12) + cos(π/12) ≈ 1.2247448714.