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Which of the following is not defined?
To determine which of the given trigonometric expressions is not defined, we analyze each option based on the definitions and properties of trigonometric functions. Step 1: Analyze each option a) cos 0° The cosine function is defined for all real numbers. The value of cos 0° is: cos 0° = 1. Thus, coRead more
To determine which of the given trigonometric expressions is not defined, we analyze each option based on the definitions and properties of trigonometric functions.
Step 1: Analyze each option
a) cos 0°
The cosine function is defined for all real numbers. The value of cos 0° is:
cos 0° = 1.
Thus, cos 0° is defined.
b) tan 45°
The tangent function is defined as tan θ = sin θ / cos θ. For θ = 45°:
tan 45° = sin 45° / cos 45° = (1/√2) / (1/√2) = 1.
Thus, tan 45° is defined.
c) sec 90°
The secant function is defined as sec θ = 1 / cos θ. For θ = 90°:
cos 90° = 0.
Since division by zero is undefined, sec 90° = 1 / cos 90° = 1 / 0 is not defined.
Thus, sec 90° is not defined.
d) sin 90°
The sine function is defined for all real numbers. The value of sin 90° is:
sin 90° = 1.
Thus, sin 90° is defined.
Step 2: Final Answer
The expression that is not defined is:
c) sec 90°.
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
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If sinθ = x and secθ = y, then tanθ is equal to
We are given: sinθ = x and secθ = y. Step 1: Recall the trigonometric identities 1. The definition of secθ is: secθ = 1/cosθ. Therefore, cosθ = 1/secθ = 1/y. 2. The definition of tanθ is: tanθ = sinθ / cosθ. Step 2: Substitute the values of sinθ and cosθ From the problem, sinθ = x and cosθ = 1/y. SuRead more
We are given:
sinθ = x and secθ = y.
Step 1: Recall the trigonometric identities
1. The definition of secθ is:
secθ = 1/cosθ.
Therefore, cosθ = 1/secθ = 1/y.
2. The definition of tanθ is:
tanθ = sinθ / cosθ.
Step 2: Substitute the values of sinθ and cosθ
From the problem, sinθ = x and cosθ = 1/y. Substituting these into the formula for tanθ:
tanθ = sinθ / cosθ
= x / (1/y)
Step 3: Simplify the expression
Dividing by 1/y is equivalent to multiplying by y:
tanθ = x * y
= xy
Step 4: Final Answer
Thus, tanθ is equal to xy.
The correct answer is:
a) xy
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/
A uniform electric field of 100 N/C exists in vertically upward direction. The decrease in electric potential as one goes up through a height of 5 cm is
The potential difference (ΔV) in a uniform electric field is given by: ΔV = − E⋅d. where: E=100N/C (electric field strength) d = 5 cm = 0.05 m (displacement in the field direction) ΔV = −(100×0.05) ΔV = −5 V Since the question asks for the decrease in potential, the answer is: (c) 5 V For more visitRead more
The potential difference (ΔV) in a uniform electric field is given by:
ΔV = − E⋅d.
where:
E=100N/C (electric field strength)
d = 5 cm = 0.05 m (displacement in the field direction)
ΔV = −(100×0.05)
ΔV = −5 V
Since the question asks for the decrease in potential, the answer is: (c) 5 V
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If 5 tanθ – 4 =0, then the value of 5 sin θ – 4 cos θ/5 sinθ + 4 cos θ is
We are given the equation: 5 tanθ - 4 = 0. Step 1: Solve for tanθ Rearrange the equation to solve for tanθ: 5 tanθ = 4 tanθ = 4/5. Step 2: Express sinθ and cosθ in terms of tanθ Using the identity tanθ = sinθ / cosθ, we can write: sinθ = 4k and cosθ = 5k, where k is a positive constant such that sinRead more
We are given the equation:
5 tanθ – 4 = 0.
Step 1: Solve for tanθ
Rearrange the equation to solve for tanθ:
5 tanθ = 4
tanθ = 4/5.
Step 2: Express sinθ and cosθ in terms of tanθ
Using the identity tanθ = sinθ / cosθ, we can write:
sinθ = 4k and cosθ = 5k,
where k is a positive constant such that sin²θ + cos²θ = 1 (Pythagorean identity).
Substitute sinθ = 4k and cosθ = 5k into the identity:
(4k)² + (5k)² = 1
16k² + 25k² = 1
41k² = 1
k² = 1/41
k = √(1/41).
Thus:
sinθ = 4k = 4/√41,
cosθ = 5k = 5/√41.
Step 3: Simplify the given expression
We are tasked with finding the value of:
(5 sinθ – 4 cosθ) / (5 sinθ + 4 cosθ).
Substitute sinθ = 4/√41 and cosθ = 5/√41 into the expression:
Numerator:
5 sinθ – 4 cosθ = 5(4/√41) – 4(5/√41)
= (20/√41) – (20/√41)
= 0.
Denominator:
5 sinθ + 4 cosθ = 5(4/√41) + 4(5/√41)
= (20/√41) + (20/√41)
= 40/√41.
Thus, the entire expression becomes:
(5 sinθ – 4 cosθ) / (5 sinθ + 4 cosθ) = 0 / (40/√41) = 0.
Step 4: Final Answer
The value of the given expression is 0.
The correct answer is:
c) zero
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/
Charge on a capacitor is doubled. Its capacity becomes k times, where
(b) k = 1 The capacitance of a capacitor is a property of the capacitor itself and does not change when the charge is altered. The capacitance is related to the physical characteristics of the capacitor, such as the area of the plates and the distance between them, not the amount of charge stored. TRead more
(b) k = 1
The capacitance of a capacitor is a property of the capacitor itself and does not change when the charge is altered. The capacitance is related to the physical characteristics of the capacitor, such as the area of the plates and the distance between them, not the amount of charge stored. Therefore, the capacitance remains the same, so k = 1.
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See lesshttps://www.tiwariacademy.com/ncert-solutions/class-12/physics/chapter-2/