Question

Sin (-7 пи)+ 2 cos 31 пи / 3 - tg 7 пи /4 С объяснением!!!!

Answer 1

Sin (-7 pi) + 2 cos (31pi/3) - tg(7pi/4)=
= sin ( - 8pi + pi) + 2* cos( 10 pi + pi/3) - tg ( 2 pi   -  pi/4) =
= sin (-pi) + 2* cos(pi/3) - tg( - pi/4) =
= 0 + 2* 1/2  - (-1) = 1 + 1 = 2

Answer 2

To solve the expression, let's break it down step by step:

1. Sin(-7π): The sine function evaluates the sine of an angle. In this case, we have -7π as the angle. The sine function is an odd function, which means sin(-θ) = -sin(θ) for any angle θ. So, sin(-7π) = -sin(7π).

2. 2 cos(31π/3): The cosine function evaluates the cosine of an angle. Here, we have 31π/3 as the angle. The cosine function is an even function, which means cos(-θ) = cos(θ) for any angle θ. So, cos(31π/3) = cos(-31π/3).

3. tg(7π/4): The tangent function evaluates the tangent of an angle. In this case, we have 7π/4 as the angle. The tangent function is also an odd function, which means tan(-θ) = -tan(θ) for any angle θ. So, tg(7π/4) = -tg(-7π/4).

Now, let's simplify each part individually:

1. -sin(7π): The sine of 7π is 0 since sin(π) = 0. Therefore, -sin(7π) = -0 = 0.

2. cos(-31π/3): The cosine function has a period of 2π, so we can subtract 2π from the angle until it lies between 0 and 2π. -31π/3 + 10π = -π/3. The cosine of -π/3 is 1/2. Therefore, cos(-31π/3) = 1/2.

3. -tg(-7π/4): Similar to cosine, the tangent function has a period of π. -7π/4 + π = -3π/4. The tangent of -3π/4 is -1 since tan(-π/4) = 1 and the tangent function is odd. Therefore, -tg(-7π/4) = -(-1) = 1.

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

0 + 2 * (1/2) - 1 = 0 + 1 - 1 = 0.

Therefore, the final result is 0.