Question

Tg1,4⋅ctg1,4+cos^2(−3π/4)−sin^2π/2−cos^2π/2

Answer 1

По действиям:
1) tg1.4*ctg1.4=1
2) cos^2(-3п/4)=cos^2 3п/4=-2/4
3) -(sin^2 п/2+cos^2 п/2)=-1
4) 1+2/4-1=2/4=0.5

Answer 2

Tg1.4*ctg1.4+cos²(-3пи/4)-sin²(пи/2)-cos²(пи/2)= 1+cos²(3пи/4)-sin²(пи/2)-cos²(пи/2) =1+(-sin(пи/4))²-1-0=1+(-√2/2)²-1=2/4=1/2

Answer 3

To simplify the expression Tg(1.4)⋅Ctg(1.4) + cos^2(-3π/4) - sin^2(π/2) - cos^2(π/2), we can break it down step by step:

1. Find the values of trigonometric functions:

   • Tan(1.4) is approximately 5.79788
   • Cot(1.4) is the reciprocal of Tan(1.4), so it's approximately 1/5.79788, which is about 0.17242.

2. Now, let's evaluate the trigonometric expressions:

   • cos^2(-3π/4) = cos^2(3π/4) since the cosine function is even.

   • cos(3π/4) = -√2/2, so cos^2(3π/4) = (-√2/2)^2 = 2/4 = 1/2.

   • sin^2(π/2) = sin^2(90 degrees) = 1 (since sin(90 degrees) is 1).

   • cos^2(π/2) = cos^2(90 degrees) = 0 (since cos(90 degrees) is 0).

3. Substitute these values back into the original expression:

   5.79788 * 0.17242 + 1/2 - 1 - 0

4. Calculate the result:

   ≈ 0.99999 + 0.5 - 1 - 0 ≈ 0.49999

So, the simplified value of the expression is approximately 0.49999.

Answer 4

Let's break down and simplify the expression step by step:

1. Start with the expression: Tg(1.4) * Ctg(1.4) + cos^2(-3π/4) - sin^2(π/2) - cos^2(π/2)

2. First, calculate the tangent and cotangent values:

   • Tan(1.4 radians) ≈ 5.79788
   • Cot(1.4 radians) ≈ 0.17294

3. Now, calculate the trigonometric functions for the other terms:

   • cos^2(-3π/4) = cos^2(3π/4) = (1/√2)^2 = 1/2
   • sin^2(π/2) = 1 (since sin(π/2) = 1)
   • cos^2(π/2) = 0 (since cos(π/2) = 0)

4. Plug the values into the expression: 5.79788 * 0.17294 + 1/2 - 1 - 0

5. Calculate the products: 0.99934 + 1/2 - 1 - 0

6. Add and subtract the values: (0.99934 + 1/2) - 1 - 0

7. Calculate the sum and subtraction: (1.49934) - 1 - 0

8. Finally, perform the remaining operations: 1.49934 - 1 = 0.49934

So, the value of the expression is approximately 0.49934.