Question

7/2sin(2П+a)-cos(3П/2+a) если a=5П/6

Answer 1

Ответ:

Пошаговое объяснение:

7/2cosa+sina=7/2cos5pi/6+sin5pi/6=-7/4подкорень(3)+1/2

Answer 2

To evaluate the expression, you need to substitute the value of "a" into the given expression and then perform the calculations. Let's go step by step:

Given expression: $\frac{7}{2}\sin(2\pi+a) - \cos\left(\frac{3\pi}{2}+a\right)$

And $a = \frac{5\pi}{6}$

Step 1: Substitute the value of "a" into the expressions:

$\sin(2\pi+a) = \sin\left(2\pi + \frac{5\pi}{6}\right)$

$\cos\left(\frac{3\pi}{2}+a\right) = \cos\left(\frac{3\pi}{2} + \frac{5\pi}{6}\right)$

Step 2: Simplify the expressions inside the trigonometric functions:

$2\pi + \frac{5\pi}{6} = \frac{12\pi}{6} + \frac{5\pi}{6} = \frac{17\pi}{6}$

$\frac{3\pi}{2} + \frac{5\pi}{6} = \frac{9\pi}{6} + \frac{5\pi}{6} = \frac{14\pi}{6} = \frac{7\pi}{3}$

Step 3: Evaluate the trigonometric functions:

$\sin\left(2\pi + \frac{5\pi}{6}\right) = \sin\left(\frac{17\pi}{6}\right) = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$

$\cos\left(\frac{3\pi}{2} + \frac{5\pi}{6}\right) = \cos\left(\frac{7\pi}{3}\right) = -\frac{\sqrt{3}}{2}$

Step 4: Substitute the values back into the original expression:

$\frac{7}{2}\sin(2\pi+a) - \cos\left(\frac{3\pi}{2}+a\right) = \frac{7}{2} \times \frac{1}{2} - \left(-\frac{\sqrt{3}}{2}\right)$

Step 5: Perform the calculations:

$\frac{7}{2} \times \frac{1}{2} = \frac{7}{4}$

Thus, the final result is:

$\frac{7}{2}\sin(2\pi+a) - \cos\left(\frac{3\pi}{2}+a\right) = \frac{7}{4} + \frac{\sqrt{3}}{2}$