F.Sc/ICS 1st Year Trigonometry MCQs

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Questions and Answers

Sin($\frac{\alpha - \pi}{2}$) is equal to which of the following?

  • sec$\alpha$
  • $-cos \alpha$ (correct)
  • $-sin \alpha$
  • cos$\alpha$

Cos$\frac{\alpha}{2}$ is equal to which of the following?

  • $\frac{1 + cos \alpha}{2}$
  • $\pm \sqrt{\frac{1 - cos \alpha}{2}}$
  • $\pm \sqrt{\frac{1 + cos \alpha}{2}}$ (correct)
  • $\frac{1 + sin \alpha}{2}$

What is the value of cos(315°)?

  • $\frac{\sqrt{3}}{2}$
  • 0
  • $\frac{1}{\sqrt{2}}$ (correct)
  • 1

2 sin 70 cos 30 is equal to which of the following?

<p>sin 100 + sin 40 (C)</p> Signup and view all the answers

What is the range of the function cos x?

<p>[-1, 1] (A)</p> Signup and view all the answers

What is the value of sin(-300°)?

<p>$\frac{\sqrt{3}}{2}$ (D)</p> Signup and view all the answers

Cos 2$\theta$ is equal to which of the following?

<p>$\frac{1 - tan^2 \theta}{1 + tan^2 \theta}$ (C)</p> Signup and view all the answers

What is the range of the cotangent function?

<p>R (C)</p> Signup and view all the answers

3sin$\alpha$ - 4sin³$\alpha$ is equal to which of the following?

<p>sin 3$\alpha$ (B)</p> Signup and view all the answers

2 sin 12° sin 46° is equal to which of the following?

<p>cos 34° - cos 58° (D)</p> Signup and view all the answers

What is the domain of sec$\theta$?

<p>$- \infty &lt; \theta &lt; + \infty$, $\theta \ne (2n + 1) \frac{\pi}{2}$, n $\in$ Z (D)</p> Signup and view all the answers

Cos 48° + cos 12° is equal to which of the following?

<p>$\sqrt{3}$ cos 36° (D)</p> Signup and view all the answers

Which of the following is equal to cos 2$\alpha$?

<p>cos$^2$$\alpha$ - sin$^2$$\alpha$ (A)</p> Signup and view all the answers

What is another way to express sin($\alpha$ + $\beta$)?

<p>sin$\alpha$cos$\beta$ + cos$\alpha$sin$\beta$ (B)</p> Signup and view all the answers

What is the value of cos 60°?

<p>$\frac{1}{2}$ (C)</p> Signup and view all the answers

What is the value of tan 45°?

<p>1 (C)</p> Signup and view all the answers

What is the reciprocal of sine?

<p>Cosecant (A)</p> Signup and view all the answers

Flashcards

sin(π/2 - α) = ?

sin(π/2 - α) is equal to cos α.

cos²(α/2) = ?

(1 + cos α) / 2 square rooted, accounting for both positive and negative roots.

cos(315°) = ?

The cosine of 315 degrees is √2 / 2.

2sin70°cos30° = ?

Applying the sum-to-product formula, 2sin(70)cos(30) can be expressed as sin(100) + sin(40).

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Range of cos(x)

The range of the cosine function, cos(x), includes all real numbers between -1 and 1, inclusive.

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sin(-300°) = ?

sin(-300°) is equal to √3 / 2.

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cos(2θ) = ?

(1 - tan²θ) / (1 + tan²θ)

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Range of cotangent function?

The range of the cotangent function is all real numbers.

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3sinα - 4sin³α = ?

3sin(α) - 4sin³(α) is equal to sin(3α).

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2sin12°sin46° = ?

2sin(12°)sin(46°) = cos(34°) - cos(58°)

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sin(-780°) = ?

sin(-780°) simplifies to -√3 / 2.

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Domain of sec(θ) = ?

The domain of sec(θ) is all real numbers except θ = (2n+1)π/2, n ∈ Z.

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cos48° + cos12° = ?

cos(48°) + cos(12°) can be simplified to √3 cos(18°).

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cos(2α) =

Multiple angle trigonometric identity: cos(2α) = cos²(α) - sin²(α)

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Study Notes

  • The document presents multiple-choice questions (MCQs) related to trigonometry for F.Sc/ICS students in their 1st year, covering topics from chapters 10 and 11.

Trigonometric Identities and Functions

  • Question 1 involves the sine function with an argument of (Ï€/2 - α).
  • Question 2 tests knowledge of cosine identities.
  • Question 3 asks for the value of cos(315°).
  • Question 5 concerns the range of the cosine function.
  • Question 6 requires simplification of sin(-300°).
  • Question 7 presents an expression for cos 2θ in terms of tan θ.
  • Question 9 involves the simplification of the expression 3sin α - 4sin³ α.
  • Question 11 asks for the value of sin(-780°).
  • Question 14 asks for the general form of cos2α

Range and Domain

  • Question 8 asks about the range of the cotangent function.
  • Question 12 pertains to the domain of the secant function.
  • Question 13 involves the simplification of cos48° + cos12°.

Trigonometric Sum and Product Formulae

  • Question 4 requires the application of sum-to-product or product-to-sum trigonometric identities to simplify 2 sin 70 cos 30.
  • Question 10 examines the conversion of a product of sines into a sum or difference: 2sin 12° sin 46°.

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