Plane And Spherical Trigonometry Quiz

1. What is the exponential form of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»log«/mi»«mi»m«/mi»«/msub»«mi»c«/mi»«mo»=«/mo»«mi»n«/mi»«/math»

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2. What is the value of Arccos(-1)

0

The value of Arccos(-1) is 180 degrees or pi radians. This is because Arccos is the inverse function of cosine, and cosine of 180 degrees or pi radians is equal to -1.

Explanation

The value of Arccos(-1) is 180 degrees or pi radians. This is because Arccos is the inverse function of cosine, and cosine of 180 degrees or pi radians is equal to -1.

3. What is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»tan«/mi»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/math»

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4. What is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»tan«/mi»«mo»§nbsp;«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/math»

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5. What is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»sin«/mi»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/math»

?

0

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6. What is the value of Arccot(0)

The value of Arccot(0) is equal to π/2. The arccotangent function is the inverse of the cotangent function. Cotangent is the ratio of the adjacent side to the opposite side in a right triangle. When the opposite side is 0, the cotangent is undefined. However, the arccotangent function returns the angle whose cotangent is equal to the given value. In this case, since the cotangent is undefined, the arccotangent is π/2.

Explanation

The value of Arccot(0) is equal to π/2. The arccotangent function is the inverse of the cotangent function. Cotangent is the ratio of the adjacent side to the opposite side in a right triangle. When the opposite side is 0, the cotangent is undefined. However, the arccotangent function returns the angle whose cotangent is equal to the given value. In this case, since the cotangent is undefined, the arccotangent is π/2.

7. What is the value of Arcsin 0?

0

The value of Arcsin 0 is 0 because the arcsine function returns the angle whose sine is equal to the given value. Since the sine of 0 is also 0, the arcsine of 0 is 0.

Explanation

The value of Arcsin 0 is 0 because the arcsine function returns the angle whose sine is equal to the given value. Since the sine of 0 is also 0, the arcsine of 0 is 0.

8. What is the value of Arccos0

0

The value of Arccos0 is 90 degrees or π/2 radians. This is because the cosine function is equal to 0 at 90 degrees or π/2 radians.

Explanation

The value of Arccos0 is 90 degrees or π/2 radians. This is because the cosine function is equal to 0 at 90 degrees or π/2 radians.

9. When expressed as a single logarithm $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msub»«mi mathvariant=¨normal¨»log«/mi»«mn»3«/mn»«/msub»«mi»b«/mi»«mo»-«/mo»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«msub»«mi mathvariant=¨normal¨»log«/mi»«mn»3«/mn»«/msub»«mi»c«/mi»«mo»-«/mo»«mn»3«/mn»«msub»«mi mathvariant=¨normal¨»log«/mi»«mn»3«/mn»«/msub»«mi»d«/mi»«/math»$ , is equal to

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10. What is x in $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»log«/mi»«mi»x«/mi»«/msub»«mn»25«/mn»«mo»=«/mo»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«/math»$ ?

5

25

125

625

The pattern in the given sequence is that each number is obtained by multiplying the previous number by 5. Starting with 5, we have 5 * 5 = 25, 25 * 5 = 125, and 125 * 5 = 625. Therefore, the missing number in the sequence is 125.

Explanation

The pattern in the given sequence is that each number is obtained by multiplying the previous number by 5. Starting with 5, we have 5 * 5 = 25, 25 * 5 = 125, and 125 * 5 = 625. Therefore, the missing number in the sequence is 125.

11. Expand $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»log«/mi»«mn»3«/mn»«/msub»«mroot»«mfrac»«mrow»«mi»c«/mi»«msup»«mi»d«/mi»«mn»2«/mn»«/msup»«/mrow»«mi»f«/mi»«/mfrac»«mn»3«/mn»«/mroot»«/math»$

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12. What is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi»c«/mi»«mi»o«/mi»«mi»t«/mi»«msqrt»«mn»3«/mn»«/msqrt»«/math»

?

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13. What is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi»c«/mi»«mi»s«/mi»«mi»c«/mi»«mo»(«/mo»«mo»-«/mo»«msqrt»«mn»2«/mn»«/msqrt»«mo»)«/mo»«/math»

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14. What is the value of $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi»c«/mi»«mi»s«/mi»«mi»c«/mi»«mfenced»«mfrac»«mrow»«mo»-«/mo»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«mn»3«/mn»«/mfrac»«/mfenced»«/math»$

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15. What is the restriction for the range of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi»c«/mi»«mi»s«/mi»«mi»c«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi»c«/mi»«mi»s«/mi»«mi»c«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»

0

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16. What is $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»sin«/mi»«mo»(«/mo»«mi mathvariant=¨normal¨»sin«/mi»«mfrac»«mrow»«mn»3«/mn»«mi»§#960;«/mi»«/mrow»«mn»4«/mn»«/mfrac»«mo»)«/mo»«/math»$

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17. What is $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»tan«/mi»«mfenced»«mrow»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»cos«/mi»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»tan«/mi»«mo»§nbsp;«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math»$

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18. 12 What is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»sec«/mi»«mo»(«/mo»«mo»-«/mo»«msqrt»«mn»2«/mn»«/msqrt»«mo»)«/mo»«/math»

«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»sec«/mi»«mo»(«/mo»«mo»-«/mo»«msqrt»«mn»2«/mn»«/msqrt»«mo»)«/mo»«/math»

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19. For what values of x is «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»log«/mi»«mi»a«/mi»«/msub»«mi»x«/mi»«mo»=«/mo»«mi»y«/mi»«/math»

X can be any real number

X can be any positive real number

X can be any nonnegative real number

X can be any positive integer

The given answer states that x can be any positive real number. This means that x can take on any value that is both positive and a real number. It does not have to be an integer or a specific value, it can be any positive real number such as 1, 2.5, or 10. This answer encompasses all possible values of x that satisfy the given conditions.

Explanation

The given answer states that x can be any positive real number. This means that x can take on any value that is both positive and a real number. It does not have to be an integer or a specific value, it can be any positive real number such as 1, 2.5, or 10. This answer encompasses all possible values of x that satisfy the given conditions.

20. What is the value of «math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»r«/mi»«mi»c«/mi»«mi mathvariant=¨normal¨»sec«/mi»«mn»2«/mn»«/math»

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