Math / Trigonometry

Question17. If converses $\sin \theta=0.14$ , find the value of $\theta$
A 10 B. $37^{\circ}$
C $48^{\circ}$ D. $59^{\circ}$

Studdy Solution

STEP 1

1. The problem involves finding the angle $\theta$ given $\sin \theta = 0.14$ .
2. The angle $\theta$ is measured in degrees.
3. We need to determine which of the given options corresponds to $\theta$ .

STEP 2

1. Use the inverse sine function to find $\theta$ .
2. Compare the calculated $\theta$ with the given options.

STEP 3

Use the inverse sine function to find $\theta$ :
$\theta = \sin^{-1}(0.14)$

STEP 4

Calculate $\theta$ using a calculator:
$\theta \approx 8.055^{\circ}$

STEP 5

Compare the calculated $\theta$ with the given options:
- A: $10^{\circ}$ - B: $37^{\circ}$ - C: $48^{\circ}$ - D: $59^{\circ}$
Since $8.055^{\circ}$ is closest to $10^{\circ}$ , the best choice is option A.
The value of $\theta$ is approximately:
$\boxed{10^{\circ}}$

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Question17. If converses $\sin \theta=0.14$ , find the value of $\theta$
A 10 B. $37^{\circ}$
C $48^{\circ}$ D. $59^{\circ}$

Studdy Solution

STEP 1

1. The problem involves finding the angle $\theta$ given $\sin \theta = 0.14$ .
2. The angle $\theta$ is measured in degrees.
3. We need to determine which of the given options corresponds to $\theta$ .

STEP 2

1. Use the inverse sine function to find $\theta$ .
2. Compare the calculated $\theta$ with the given options.

STEP 3

Use the inverse sine function to find $\theta$ :
$\theta = \sin^{-1}(0.14)$

STEP 4

Calculate $\theta$ using a calculator:
$\theta \approx 8.055^{\circ}$

STEP 5

Compare the calculated $\theta$ with the given options:
- A: $10^{\circ}$ - B: $37^{\circ}$ - C: $48^{\circ}$ - D: $59^{\circ}$
Since $8.055^{\circ}$ is closest to $10^{\circ}$ , the best choice is option A.
The value of $\theta$ is approximately:
$\boxed{10^{\circ}}$

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Question17. If converses sin⁡θ=0.14\sin \theta=0.14sinθ=0.14, find the value of θ\thetaθA 10 B. 37∘37^{\circ}37∘C 48∘48^{\circ}48∘ D. 59∘59^{\circ}59∘

Studdy Solution

STEP 1

1. The problem involves finding the angle θ\thetaθ given sin⁡θ=0.14\sin \theta = 0.14sinθ=0.14.2. The angle θ\thetaθ is measured in degrees.3. We need to determine which of the given options corresponds to θ\thetaθ.

STEP 2

1. Use the inverse sine function to find θ\thetaθ.2. Compare the calculated θ\thetaθ with the given options.

STEP 3

Use the inverse sine function to find θ\thetaθ:θ=sin⁡−1(0.14) \theta = \sin^{-1}(0.14) θ=sin−1(0.14)

STEP 4

Calculate θ\thetaθ using a calculator:θ≈8.055∘ \theta \approx 8.055^{\circ} θ≈8.055∘

STEP 5

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Start learning now

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Question17. If converses $\sin \theta=0.14$ , find the value of $\theta$
A 10 B. $37^{\circ}$
C $48^{\circ}$ D. $59^{\circ}$

1. The problem involves finding the angle $\theta$ given $\sin \theta = 0.14$ .
2. The angle $\theta$ is measured in degrees.
3. We need to determine which of the given options corresponds to $\theta$ .

1. Use the inverse sine function to find $\theta$ .
2. Compare the calculated $\theta$ with the given options.

Use the inverse sine function to find $\theta$ :
$\theta = \sin^{-1}(0.14)$

Calculate $\theta$ using a calculator:
$\theta \approx 8.055^{\circ}$