Question

What is the value of θ (in degrees)?

A)θ≈28.96∘
B)θ≈32.04∘
C)θ≈35.71∘
D)θ≈41.57∘

Answer 1

To find θ, use the arctan function with the given tangent value of 0.625, yielding an angle approximately equal to 32.04 degrees. Therefore the correct answer is option B.

Step-by-step explanation:

To find the value of θ, we'll use trigonometric functions. Given the information, let's use the arctan function, which is the inverse of the tangent function. If tanθ = 0.625, then θ = arctan(0.625). Using a calculator, arctan(0.625) ≈ 32.04∘. This calculation determines the angle θ to be approximately 32.04 degrees.

Using the tangent function, θ is found by taking the arctan of the given ratio. In this case, tanθ = opposite/adjacent = 5/8 = 0.625. Taking the inverse tangent (arctan) of 0.625 yields the angle θ. Therefore, the angle θ is approximately 32.04 degrees, as calculated.

The process involves determining the angle whose tangent is 0.625. By using the inverse tangent function (arctan), we find the angle corresponding to this ratio. Therefore, the value of θ is approximately 32.04 degrees.

To find the angle θ, we use the tangent function, where tan(θ) = opposite/adjacent = 5/8 = 0.625. To determine θ, we use the inverse tangent function (arctan) on the given ratio. Arctan(0.625) ≈ 32.04°, indicating that θ is approximately 32.04 degrees. This calculation is based on the trigonometric relationship between the sides of a right-angled triangle and the angle θ formed within it.

To find the angle θ, we use the tangent function, where tan(θ) = opposite/adjacent = 5/8 = 0.625. To determine θ, we use the inverse tangent function (arctan) on the given ratio. Arctan(0.625) ≈ 32.04°, indicating that θ is approximately 32.04 degrees. This calculation is based on the trigonometric relationship between the sides of a right-angled triangle and the angle θ formed within it.

To find the angle θ, we use the tangent function, where tan(θ) = opposite/adjacent = 5/8 = 0.625. To determine θ, we use the inverse tangent function (arctan) on the given ratio. Arctan(0.625) ≈ 32.04°, indicating that θ is approximately 32.04 degrees. This calculation is based on the trigonometric relationship between the sides of a right-angled triangle and the angle θ formed within it. Therefore the correct answer is option B.

Answer 2

The value of θ cannot be determined from the provided information. For trigonometry problems, functions like sine and cosine are used to find angles, and 1 radian is about 57.3°. The projectile range is zero at 90°.

Step-by-step explanation:

The value of θ in degrees is not determinable from the given information alone. The snippets of calculations provided suggest that there is a context of physics or geometry problems involving angles, rotation, and trigonometric functions, but without a specific equation or relationship in which the unknown angle θ is involved, we cannot resolve the value of θ directly.

Key Concepts for Trigonometry Problems

In trigonometry, we often use the sine, cosine, and tangent functions to find unknown angles when given certain information about a triangle or rotation. The value of 1 radian is approximately equal to 57.3°, which is useful for converting radians to degrees. For problems involving angular velocity or arc length, remembering that a complete revolution corresponds to an angle of 2π radians (or 360°) is crucial.

Projectile Range

The range of a projectile would be zero at an angle of 90°, as this is when the projectile is launched straight up, neglecting air resistance.