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Business Mathematics and Basic Statistics · Class 11 Commerce

Ch 6Trigonometry — Class 11 Business Mathematics and Basic Statistics, concept-first.

Trigonometry is the branch of mathematics that studies the relationship between the angles and the sides of a triangle. In the WBCHSE Class 11 Commerce Business Mathematics and Basic Statistics syllabus, trigonometry is a compact, self-contained unit that builds the angle-ratio toolkit used later whenever an angle-base…

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Q&A

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Concepts

~6m

Unit weightage

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Key concepts

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Ratios of Standard Angles

The angles have exact, memorisable trigonometric ratio values, derived from an isosceles right triangle () and a bisected equilateral triangle (/), with and as limiting cases.

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Chapter contents

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1

Trigonometric Ratios

Trigonometry is the branch of mathematics that studies the relationship between the angles and the sides of a triangle.

2

Ratios of Standard Angles (0°, 30°, 45°, 60°, 90°)

Five angles — — appear so often in numerical work that their trigonometric ratios are worth memorising as a single reference table rather than recomputed from a triangle every time.

3

The Pythagorean Identity and Derived Identities

In the right triangle used to define the trigonometric ratios, the Pythagorean theorem states . Dividing every term by gives

4

Complementary and Supplementary Angle Relations

Two angles are complementary if they add up to , and supplementary if they add up to . Both relationships give useful shortcuts for rewriting one trigonometric ratio in terms of another, without any n…

5

Ratios of Angles Beyond 90° — 120°, 135°, 150°, 180°

Each of can be written as minus a standard angle already in the table:

Exercises

+Show 6 questions6 questions
  1. Q8Evaluate: $2\sin^230° + 3\cos^260° - \tan^245°$.Free
  2. Q9If $\sin\theta = \dfrac{5}{13}$ and $\theta$ is an acute angle, find $\cos\theta$ and $\sec\theta$.Free
  3. Q10Prove that: $(\sec\theta - \tan\theta)(\sec\theta + \tan\theta) = 1$.Preview
  4. Q11Using the complementary-angle relation, evaluate: $\dfrac{\cos80°}{\sin10°}$.Preview
  5. Q12Find the value of: $\tan135° + \cot150°$.Preview
  6. Q13Find the value of: $\sin^2120° + \cos^2150°$.Preview

More questions

+Show 7 questions7 questions
  1. Example 1In a right-angled triangle, the side opposite to angle $\theta$ measures 3 units, the side adjacent to $\theta$ measures 4 units, and the hy…Free
  2. Example 2Evaluate: $\sin30°\cos60° + \cos30°\sin60°$.Free
  3. Example 3Evaluate: $(\sin45° + \cos45°)^2$.Free
  4. Example 4If $\cos\theta = \dfrac{3}{5}$ and $\theta$ is an acute angle, find $\sin\theta$ and $\tan\theta$.Preview
  5. Example 5Prove that: $(1-\cos^2\theta)(1+\cot^2\theta) = 1$.Preview
  6. Example 6Simplify: $\sin(90°-\theta)\cdot\sec\theta$.Preview
  7. Example 7Find the value of: $\sin150° + \cos120°$.Preview