cos(θ) = √(1 - sin²(θ)) = √(1 - 0.36) = √0.64 = 0.8

θ = arcsin(0.6) ≈ 36.87°, rounded to 37°

θ = sin⁻¹(0.8) ≈ 53.13°

tan(x) = 1 at x = 45° and 225°; in the interval [0°, 360°), the first solution is 45°.

Using the identity tan(θ) = sin(θ)/cos(θ), we find sin(θ) = 3/5.

Mean = (22 + 24 + 26 + 28 + 30) / 5 = 130 / 5 = 26.

Using tan(30) = height / 20, height = 20 * tan(30) = 20 * (1/√3) = 20/√3 = 10√3 meters.

Using tan(30°) = height/40, height = 40 * (1/√3) = 40/√3 = 20√3 meters.

The angle subtended at the circumference is half of that at the center. Therefore, it is 60 degrees / 2 = 30 degrees.

In a 30-60-90 triangle, the longest side (hypotenuse) is twice the shortest side: 2 * 5 = 10 cm.

Area = πr², so r = √(Area/π) = √(50.24/π) ≈ 4 cm.

The area of a sector is given by (θ/2) * r². Thus, 20π = (θ/2) * 10². Solving gives θ = 4 radians.

Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 36) / 12 = 6 cm.

Area = 1/2 * base * height. Thus, 24 = 1/2 * 8 * height. Therefore, height = 24 / 4 = 6 cm.

Area = 1/2 * base * height; if base is doubled, area = 1/2 * (2 * base) * height = 2 * (1/2 * base * height).

The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.

The slope is calculated as (y2 - y1) / (x2 - x1). Here, it is (7 - 3) / (2 - 2), which is undefined since the denominator is 0.

Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(5 - 2)² + (7 - 3)²] = √[3² + 4²] = √25 = 5 units.

Slope = (y2 - y1) / (x2 - x1) = (7 - 3) / (5 - 2) = 4/3.

Using the distance formula: d = √((x+4 - x)² + (y+3 - y)²) = √(4² + 3²) = √(16 + 9) = √25 = 5.

Using the midpoint formula: D = ((x1 + x2)/2, (y1 + y2)/2). Solving gives F(7, 9).

The length of line segment AB is the difference in the y-coordinates: |7 - 3| = 4.

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Here, distance = √((2 - 2)² + (7 - 3)²) = √(0 + 16) = 4.

Distance AB = √((5-2)² + (7-3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Length AB = √((5 - 2)² + (7 - 3)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

The slope is calculated as (y2 - y1) / (x2 - x1). Here, it is (5 - 2) / (1 - 1), which is undefined.

Distance AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.

The distance between two points (x1, y1) and (x2, y2) is given by the formula: √((x2 - x1)² + (y2 - y1)²). Thus, distance = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.