Question

1) 3cos^2x-2sin^2x при sin^2x=0,7 2) cos2=3/5; 0 < x < П/2, найдите ctg x; 3) sin x = 3v11/10, П/2 < x < П, найдите cos x; 4) 57v2 × cos 405°; 5) Вычислите: 18v2 × sin (-45°) × tg (-30°) × cos (-30°)

Answer 1

I hope this helps you

Answer 2

To solve the given trigonometric expressions, we'll use the given information and trigonometric identities. Let's go step by step:

1. Given expression: 3cos^2x - 2sin^2x Given sin^2x = 0.7

We know the trigonometric identity: sin^2x + cos^2x = 1

Rearrange the identity to get cos^2x = 1 - sin^2x Substitute sin^2x = 0.7 into the equation: cos^2x = 1 - 0.7 cos^2x = 0.3

Now, we want to find cosx, which is the positive square root of cos^2x: cosx = √(0.3) ≈ 0.5477

2. Given expression: cos^2x = 3/5 We are given that 0 < x < π/2, and we need to find cot(x).

We know the trigonometric identity: cot^2x = 1 + tan^2x

Rearrange the identity to get tan^2x = cot^2x - 1

Substitute the given value cos^2x = 3/5 into the identity: tan^2x = (1 / cos^2x) - 1 tan^2x = (1 / (3/5)) - 1 tan^2x = (5/3) - 1 tan^2x = (5 - 3) / 3 tan^2x = 2 / 3

Now, we want to find cot(x), which is the reciprocal of tan(x): cot(x) = 1 / tan(x) = 1 / √(tan^2x) = 1 / √(2/3) = √(3/2) / 2 ≈ 0.8660

3. Given expression: sin(x) = 3√11 / 10 We are given that π/2 < x < π, and we need to find cos(x).

We know the trigonometric identity: sin^2x + cos^2x = 1

Rearrange the identity to get cos^2x = 1 - sin^2x

Substitute the given value sin(x) = 3√11 / 10 into the equation: cos^2x = 1 - (3√11 / 10)^2 cos^2x = 1 - (99/100) cos^2x = 1/100

Now, we want to find cos(x), which is the positive square root of cos^2x: cos(x) = √(1/100) = 1/10

4. Given expression: 57√2 × cos 405° First, convert 405° to its equivalent angle in the first quadrant (0° to 90°) since cosine is positive in the first quadrant and has the same value in the fourth quadrant. 405° - 360° = 45°

Now, we know cos(45°) = √2 / 2, so the expression becomes: 57√2 × (√2 / 2) = 57/2

5. Given expression: 18√2 × sin(-45°) × tan(-30°) × cos(-30°)

We know the following trigonometric values: sin(-45°) = -√2 / 2 tan(-30°) = -1 / √3 cos(-30°) = √3 / 2

Now, let's substitute these values into the expression: 18√2 × (-√2 / 2) × (-1 / √3) × (√3 / 2)

Many terms cancel out: 18 × (-1) × (-1) × (1) = 18

So, the result is 18.