Question

5sin п/4 +3 tg п/4-5 cos п/4 -10 ctg п/6

Answer 1

$5\, sin\frac{\pi}{4}+3\, tg\frac{\pi}{4}-5\, cos\frac{\pi}{4}-10\, ctg\frac{\pi}{6}=\\\\=5\cdot \frac{\sqrt2}{2}+3\cdot 1-5\cdot \frac{\sqrt2}{2}-10\cdot \sqrt3=3-10\sqrt3=\sqrt3\cdot (\sqrt3-10)$

Answer 2

To solve this expression, we need to evaluate each trigonometric function at its respective angle and then perform the arithmetic operations. Let's break it down step by step:

1. Calculate sin(π/4): sin(π/4) = √2 / 2 ≈ 0.7071

2. Calculate tan(π/4): tan(π/4) = 1

3. Calculate cos(π/4): cos(π/4) = √2 / 2 ≈ 0.7071

4. Calculate cot(π/6): cot(π/6) = 1 / tan(π/6) = 1 / (√3 / 3) = √3 / 3 ≈ 0.5774

Now, let's substitute these values back into the original expression:

5sin(π/4) + 3tan(π/4) - 5cos(π/4) - 10cot(π/6)

= 5 * 0.7071 + 3 * 1 - 5 * 0.7071 - 10 * 0.5774

Now, let's calculate the values:

= 3.5355 + 3 - 3.5355 - 5.774

= 6 - 9.3095

= -3.3095

Therefore, the value of the expression is approximately -3.3095.