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What is the value of sin-1(-x) for all x belongs to [-1, 1]?
- a)-sin-1(x)
- b)sin-1(x)
- c)2sin-1(x)
- d)sin-1(-x)/2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
What is the value of sin-1(-x) for all x belongs to [-1, 1]?a)-sin-1(x...
Answer:
To find the value of sin^(-1)(-x) for all x belongs to [-1, 1], let's go through the step-by-step process:
Step 1: Recall the definition of sin^(-1)(x) or arcsin(x):
The value of sin^(-1)(x) is the angle whose sine is x. In other words, if y = sin^(-1)(x), then sin(y) = x.
Step 2: Substitute -x into the equation:
sin^(-1)(-x) = y, where sin(y) = -x.
Step 3: Use the property of sin(-θ) = -sin(θ):
Since sin(y) = -x, we can rewrite it as sin(-y) = x.
Step 4: Apply the definition of sin^(-1)(x) to the equation:
sin^(-1)(x) = -y.
Step 5: Simplify the equation:
Since sin^(-1)(x) = -y, we can rewrite it as -sin^(-1)(x) = y.
Step 6: Substitute -x into the equation:
-sin^(-1)(x) = y, where sin(y) = -x.
Conclusion:
Therefore, the value of sin^(-1)(-x) for all x belongs to [-1, 1] is -sin^(-1)(x). Hence, option 'A' is the correct answer.
To find the value of sin^(-1)(-x) for all x belongs to [-1, 1], let's go through the step-by-step process:
Step 1: Recall the definition of sin^(-1)(x) or arcsin(x):
The value of sin^(-1)(x) is the angle whose sine is x. In other words, if y = sin^(-1)(x), then sin(y) = x.
Step 2: Substitute -x into the equation:
sin^(-1)(-x) = y, where sin(y) = -x.
Step 3: Use the property of sin(-θ) = -sin(θ):
Since sin(y) = -x, we can rewrite it as sin(-y) = x.
Step 4: Apply the definition of sin^(-1)(x) to the equation:
sin^(-1)(x) = -y.
Step 5: Simplify the equation:
Since sin^(-1)(x) = -y, we can rewrite it as -sin^(-1)(x) = y.
Step 6: Substitute -x into the equation:
-sin^(-1)(x) = y, where sin(y) = -x.
Conclusion:
Therefore, the value of sin^(-1)(-x) for all x belongs to [-1, 1] is -sin^(-1)(x). Hence, option 'A' is the correct answer.
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Community Answer
What is the value of sin-1(-x) for all x belongs to [-1, 1]?a)-sin-1(x...
Let, θ = sin-1(-x)
So, -π/2 ≤ θ ≤ π/2
⇒ -x = sinθ
⇒ x = -sinθ
⇒ x = sin(-θ)
Also, -π/2 ≤ -θ ≤ π/2
⇒ -θ = sin-1(x)
⇒ θ = -sin-1(x)
So, sin-1(-x) = -sin-1(x)
So, -π/2 ≤ θ ≤ π/2
⇒ -x = sinθ
⇒ x = -sinθ
⇒ x = sin(-θ)
Also, -π/2 ≤ -θ ≤ π/2
⇒ -θ = sin-1(x)
⇒ θ = -sin-1(x)
So, sin-1(-x) = -sin-1(x)
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What is the value of sin-1(-x) for all x belongs to [-1, 1]?a)-sin-1(x)b)sin-1(x)c)2sin-1(x)d)sin-1(-x)/2Correct answer is option 'A'. Can you explain this answer?
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