Skip to content
← Business Mathematics and Statistics

Business Mathematics and Statistics · Class 11 Commerce

Ch 4Trigonometry — Class 11 Business Mathematics and Statistics, concept-first.

In trigonometry, an angle is generated by the rotation of a ray from an initial position (the initial side) to a final position (the terminal side), both sharing a common starting point called the vertex.

36

Q&A

6

Concepts

Not available

Exam weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Degree-Radian Conversion and Standard Position of Angles

An angle can be measured in two equivalent systems: sexagesimal (degree) measure, where a full rotation is , and radian measure, where a full rotation is radians.

Most relevant Q&A

Start with this concept →

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Angles and Their Measurement

In trigonometry, an angle is generated by the rotation of a ray from an initial position (the initial side) to a final position (the terminal side), both sharing a common starting point called the ver…

2

Trigonometric Ratios and Signs in the Four Quadrants

Place an angle in standard position and let be any point (other than the origin) on its terminal side, at distance from the origin.

3

Fundamental (Pythagorean) Identities

The three Pythagorean (fundamental) identities connect the trigonometric ratios of the same angle and hold for every value of for which the ratios involved are defined.

4

Trigonometric Ratios of Standard Angles

The trigonometric ratios of five standard angles — — come up so often in problem-solving that they are worth memorising outright rather than recomputing every time.

5

Compound Angle Formulae

A compound angle is an angle expressed as the algebraic sum or difference of two (or more) angles, such as or . Importantly, is not equal to — the correct expansions are the compound angle formulae:

6

Multiple and Sub-multiple Angles

Setting in the compound-angle formulae of the previous section gives the double-angle (multiple-angle) formulae:

7

Trigonometric Equations and General Solutions

A trigonometric equation is an equation involving trigonometric ratios of an unknown angle, such as . Because every trigonometric ratio is periodic, such an equation is satisfied not by a single value…

Exercises

+Show 6 questions6 questions
  1. Q2Convert $\dfrac{7\pi}{6}$ radians into degree measure.Free
  2. Q5Determine the sign of $\cos200^\circ$ and $\tan320^\circ$, without using a calculator.Free
  3. Q8If $\sec\theta+\tan\theta=5$, find the value of $\sec\theta-\tan\theta$.Preview
  4. Q10Find the value of $\cos15^\circ$ using the compound angle formula.Preview
  5. Q13If $\cos\theta=\dfrac{5}{13}$ and $\theta$ is acute, find the value of $\tan2\theta$.Preview
  6. Q16Solve $\sqrt3\tan\theta-1=0$ for the general solution, and hence list every solution with $0\le\theta<2\pi$.Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 20 questions20 questions
  1. Q1If $\sin A + \cos A = 1$ then $\sin 2A$ is equal to : (a) $\dfrac{1}{2}$ (b) $1$ (c) $2$ (d) $0$Preview
  2. Q2Show that $\dfrac{\sin 2\theta}{1 + \cos 2\theta} = \tan\theta$.Preview
  3. Q3If $\tan\alpha = \dfrac{1}{3}$ and $\tan\beta = \dfrac{1}{7}$ then prove that $(2\alpha + \beta) = \dfrac{\pi}{4}$.Preview
  4. Q4(a) Prove that $\sin 600° \cos 390° + \cos 480° \sin 150° = -1$. OR (b) Solve the following linear programming problem by graphical method :…Preview
  5. Q5The degree measure of $\dfrac{\pi}{8}$ is : (a) $22^\circ 60'$ (b) $20^\circ 60'$ (c) $20^\circ 30'$ (d) $22^\circ 30'$Preview
  6. Q6The radian measure of $37^\circ 30'$ is : (a) $\dfrac{7\pi}{24}$ (b) $\dfrac{5\pi}{24}$ (c) $\dfrac{9\pi}{24}$ (d) $\dfrac{3\pi}{24}$Preview
  7. Q7Find the value of $\cot 75^\circ$.Preview
  8. Q8If three angles A, B and C are in arithmetic progression, prove that $\cot B = \dfrac{\sin A - \sin C}{\cos C - \cos A}$.Preview
  9. Q9The value of $\sin 15^\circ \cos 15^\circ$ is : (a) $\dfrac{\sqrt{3}}{2}$ (b) $1$ (c) $\dfrac{1}{4}$ (d) $\dfrac{1}{2}$Preview
  10. Q10If $p \sec 50^\circ = \tan 50^\circ$, then the value of p is : (a) $\tan 50^\circ$ (b) $\cos 50^\circ$ (c) $\sec 50^\circ$ (d) $\sin 50^\cir…Preview
  11. Q11Find the value of $\tan 150^\circ$.Preview
  12. Q12Show that $\tan^{-1}\left(\dfrac{1}{2}\right) + \tan^{-1}\left(\dfrac{2}{11}\right) = \tan^{-1}\left(\dfrac{3}{4}\right)$.Preview
  13. Q13If $\tan A=\dfrac{1}{2}$ and $\tan B=\dfrac{1}{3}$ then $\tan(2A+B)$ is equal to : (a) $3$ (b) $1$ (c) $4$ (d) $2$Preview
  14. Q14The value of $\sin(-420^\circ)$ is : (a) $\dfrac{1}{2}$ (b) $\dfrac{\sqrt{3}}{2}$ (c) $\dfrac{-1}{2}$ (d) $\dfrac{-\sqrt{3}}{2}$Preview
  15. Q15Find the value of $\tan 75^\circ$.Preview
  16. Q16Prove that $\tan^{-1}\left(\dfrac{2}{11}\right)+\tan^{-1}\left(\dfrac{7}{24}\right)=\tan^{-1}\left(\dfrac{1}{2}\right)$Preview
  17. Q17The value of $4\cos^3 40°-3\cos 40°$ is : (a) $\dfrac{1}{2}$ (b) $\dfrac{\sqrt{3}}{2}$ (c) $\dfrac{1}{\sqrt{2}}$ (d) $-\dfrac{1}{2}$Preview
  18. Q18If $A=30°$ then prove that $\sin 2A=\dfrac{2\tan A}{1+\tan^2 A}$Preview
  19. Q19Prove that $\dfrac{\sin(B-C)}{\cos B\cos C}+\dfrac{\sin(C-A)}{\cos C\cos A}+\dfrac{\sin(A-B)}{\cos A\cos B}=0$Preview
  20. Q20(a) Prove that $(\cos\alpha+\cos\beta)^2+(\sin\alpha+\sin\beta)^2=4\cos^2\left(\dfrac{\alpha-\beta}{2}\right)$. OR (b) The following table g…Preview

More questions

+Show 10 questions10 questions
  1. Example 1Convert $75^\circ$ into radian measure.Free
  2. Example 3The angles of a triangle are in the ratio $2:3:4$. Express each angle in radian measure.Free
  3. Example 4If $\sin\theta = \dfrac{3}{5}$ and $\theta$ lies in the second quadrant, find $\cos\theta$ and $\tan\theta$.Free
  4. Example 6Find the value of $\sin(-30^\circ)+\cos(-60^\circ)$.Preview
  5. Example 7Prove that $(1-\cos^2\theta)(1+\cot^2\theta) = 1$.Preview
  6. Example 9Using the compound angle formula, find the value of $\sin75^\circ$.Preview
  7. Example 11If $\tan A=\dfrac12$ and $\tan B=\dfrac13$, find the value of $\tan(A+B)$.Preview
  8. Example 12If $\sin\theta=\dfrac{3}{5}$ and $\theta$ is acute, find the values of $\sin2\theta$ and $\cos2\theta$.Preview
  9. Example 14Express $\sin3A$ in terms of $\sin A$ only.Preview
  10. Example 15Solve $2\sin\theta-1=0$ and write the general solution.Preview