Question

2cos(-45) + sin 405 - tg(-540) 2si(-π/6) + cos 13π/3 +ctg(-5π/2)

Answer 1

$2Cos(-45)+Sin405-tg(-540)=2Cos45 +Sin(360+45)+$ $tg(180*3+0)= 2Cos45 +Sin45 +tg0=2* \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2}+0= \sqrt{2} + \frac{ \sqrt{2} }{2}$ $= \frac{3 \sqrt{2} }{2}$

$2Sin(- \frac{ \pi }{6})+Cos \frac{13 \pi }{3}+Ctg(- \frac{5 \pi }{2})=-2Sin \frac{ \pi }{6} +Cos(4 \pi + \frac{ \pi }{3})-Ctg(4 \pi +$ $\frac{ \pi }{2})= - 2* \frac{1}{2} +Cos \frac{ \pi }{3}-Ctg \frac{ \pi }{2}=-1+ \frac{1}{2}-0=-0,5$

Answer 2

To simplify the given expression, let's evaluate each term step by step:

1. Evaluating 2cos(-45): The cosine function is an even function, which means cos(-x) = cos(x). Therefore, cos(-45) = cos(45) = (√2)/2 Therefore, 2cos(-45) = 2 * (√2)/2 = √2

2. Evaluating sin(405): Since sine is a periodic function with a period of 360 degrees (or 2π radians), we can subtract multiples of 360 degrees from the given angle to find an equivalent angle within one period. 405 degrees = 360 degrees + 45 degrees sin(405) = sin(45) = (√2)/2

3. Evaluating tg(-540): The tangent function has a period of 180 degrees (or π radians). Therefore, we can subtract multiples of 180 degrees from the given angle to find an equivalent angle within one period. -540 degrees = -540 degrees + 3 * 180 degrees = 180 degrees tg(-540) = tg(180) = 0

4. Evaluating 2sin(-π/6): The sine function is an odd function, which means sin(-x) = -sin(x). Therefore, sin(-π/6) = -sin(π/6) = -1/2 Therefore, 2sin(-π/6) = 2 * (-1/2) = -1

5. Evaluating cos(13π/3): We can simplify the given angle: 13π/3 = (12π + π/3) The cosine function has a period of 2π, so we can subtract multiples of 2π from the given angle to find an equivalent angle within one period. cos(13π/3) = cos(π/3) = 1/2

6. Evaluating ctg(-5π/2): The cotangent function is the reciprocal of the tangent function. Since we found tg(-540) to be 0, the cotangent function will be undefined at that point.

Now, let's substitute the values we found into the expression:

√2 + (√2)/2 - 0 - 1 + 1/2 + undefined

Simplifying this expression, we get:

√2 + (√2)/2 - 1/2 + undefined

Therefore, the simplified expression is √2 + (√2)/2 - 1/2 + undefined.