Trigonometric Function MCQ Quiz - Objective Question with Answer for Trigonometric Function - Download Free PDF
Last updated on May 3, 2025
Latest Trigonometric Function MCQ Objective Questions
Trigonometric Function Question 1:
Find
Answer (Detailed Solution Below)
Trigonometric Function Question 1 Detailed Solution
Concept:
Calculation:
Given: y =
As we know that,
So,
Differentiating with respect to x, we get
Trigonometric Function Question 2:
If
Answer (Detailed Solution Below)
Trigonometric Function Question 2 Detailed Solution
Let,
Now,
Trigonometric Function Question 3:
If
Answer (Detailed Solution Below)
Trigonometric Function Question 3 Detailed Solution
Concept:
Inverse Tangent and Cotangent Relationships:
- The inverse cotangent function can be written in terms of the inverse tangent function: cot-1 θ = (π/2) - tan-1 θ.
- This relationship is useful in simplifying equations involving both tan-1 and cot-1.
Calculation:
Given the equation:
tan-1 (2 / (3x + 1)) = cot-1 (3 / (3x + 1))
We use the identity cot-1 θ = (π/2) - tan-1 θ to rewrite the equation as:
tan-1 (2 / (3x + 1)) = (π/2) - tan-1 (3 / (3x + 1))
Taking the tangent of both sides:
(2 / (3x + 1)) = (3 / (3x + 1))
This leads to the contradictory equation:
2 = 3
Therefore, there is no solution to this equation.
Conclusion:
The correct answer is:
- Option (1): There is no real value of x satisfying the above equation.
Trigonometric Function Question 4:
If
Answer (Detailed Solution Below)
Trigonometric Function Question 4 Detailed Solution
Calculation
Given:
Squaring both sides:
⇒
Differentiating both sides with respect to x:
⇒
⇒
⇒
⇒
Hence option 1 is correct.
Trigonometric Function Question 5:
If
Answer (Detailed Solution Below)
Trigonometric Function Question 5 Detailed Solution
Calculation
⇒
⇒
⇒
⇒
⇒
Substitute x = 0 and y = 1:
⇒
⇒
⇒
⇒
∴
Hence option 2 is correct
Top Trigonometric Function MCQ Objective Questions
If y = tan (cot−1 x), then
Answer (Detailed Solution Below)
Trigonometric Function Question 6 Detailed Solution
Download Solution PDFConcept:
tan (tan-1 x) = x
Calculation:
Given:
y = tan (cot−1 x)
⇒ y = 1/x (∵tan (tan-1 x) = x)
Differentiating with respect to x, we get
At x = 1
Differentiate
Answer (Detailed Solution Below)
Trigonometric Function Question 7 Detailed Solution
Download Solution PDFConcept:
----(1)- da/dx = 0, where a is any constant
----(2)-
Calculation:
Answer (Detailed Solution Below)
Trigonometric Function Question 8 Detailed Solution
Download Solution PDFGiven:
? =
Formula:
sin (90 - θ) = cos θ
tan (90 - θ) = cot θ
Calculation:
⇒ sin 33°. cos57° = sin(90° - 57°).cos57° = cos57°.cos57° = cos257°
⇒ sec 62°.sin28° = 1/cos 62° × sin 28° = sin (90° - 62°) × 1/cos 62°
= cos62° × 1/cos 62° = 1
⇒ cos33°. sin 57° = sin (90° - 33°) . sin 57° = sin257°
⇒ cosec 62°. cos 28° = cos 28° × 1/sin 62°
= cos 28° × 1/sin(90° - 28°)
= cos 28°/cos 28° = 1
⇒ tan 15°.tan 35°.tan 60°.tan 55°.tan 75° = (sin15°/cos15°) × (sin75°/cos75°) × (sin55°/cos55° ) × (sin35°/cos35°) × √3
= √3
Then,
⇒ ? = (cos257° + 1 + sin257° + 1)/√3
⇒ ? = 3/√3
⇒ ? = √3
∴
Answer (Detailed Solution Below)
Trigonometric Function Question 9 Detailed Solution
Download Solution PDFConcept:
Suppose that we have two functions f(x) and g(x) and they are both differentiable.
- Chain Rule:
- Product Rule:
Calculation:
We have to find the value of
If y =
Answer (Detailed Solution Below)
Trigonometric Function Question 10 Detailed Solution
Download Solution PDFConcept:
Derivatives of Trigonometric Functions:
Trigonometric Formulae:
Chain Rule of Derivatives:
. .
Calculation:
We have y =
Let x = tan2 z.
∴ y =
Now, differentiating w.r.t. z, we get:
Using the chain rule of derivatives, we get:
Find all values of x in the interval [0, 2π] such that sin x = sin 2x?
Answer (Detailed Solution Below)
Trigonometric Function Question 11 Detailed Solution
Download Solution PDFConcept-
sin 2x = 2sin x cos x.
Calculation-
As sin x = sin 2x
⇒ sin 2x - sin x = 0
⇒ 2 sin x cos x - sin x = 0
⇒ sin x (2cos x - 1) = 0
So either sin x = 0 , in interval [0, 2π] when x = 0, π, 2π
or 2cos x -1 = 0, i.e cos x =
∴ total values of x in interval [0, 2π] is 5.
If y =
Answer (Detailed Solution Below)
Trigonometric Function Question 12 Detailed Solution
Download Solution PDFConcept used:
Trigonometry formula
sin 2x = 2sin x cos x
Calculation:
y =
y =
⇒ y =
⇒ y =
⇒ y =
Differentiate both sides, we get
⇒
⇒
Find
Answer (Detailed Solution Below)
Trigonometric Function Question 13 Detailed Solution
Download Solution PDFConcept:
Calculation:
Given: y =
As we know that,
So,
Differentiating with respect to x, we get
If y = sin (cos2 x2), then
Answer (Detailed Solution Below)
Trigonometric Function Question 14 Detailed Solution
Download Solution PDFConcept:
Derivatives of Trigonometric Functions:
Chain Rule of Derivatives:
. .
Calculation:
We have y = sin (cos2 x2)
Differentiating w.r.t. x, we get:
= -4xcos (cos2 x2) cos x2 sin x2
If f(x) = log x + 3x - 10 and g(x) = tanx then find fog'(x)
Answer (Detailed Solution Below)
Trigonometric Function Question 15 Detailed Solution
Download Solution PDFConcept:
fog(x) = f{g(x)}
Calculation:
f(x) = log x + 3x - 10 and g(x) = tanx
fog(x) = f{g(x)} = log(tanx) + 3tanx - 10
⇒ fog'(x) =
⇒ fog'(x) =
⇒ fog'(x) =
⇒ fog'(x) =
⇒ fog'(x) =
⇒ fog'(x) =