Class 11 Maths · Original EZT practice
Trigonometric Functions (Class 11 Chapter 3): summary and practice
Class 11 trigonometry rebuilds the ratios on any angle, not just acute ones: radians replace degrees, signs change by quadrant, and the sum-and-difference formulas unlock exact values like sin 75. All questions are original EZT tutor practice following the chapter's own section order.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Angles: degree and radian measure
A full circle is 360 degrees or 2pi radians, so pi rad = 180 degrees and 1 radian is about 57.30 degrees. The arc-length formula l = r theta needs theta in radians.
2. Trigonometric functions and their signs
Defined on the unit circle, the ratios extend to every angle. Signs follow the quadrant: all positive in the first, sin in the second, tan in the third, cos in the fourth.
3. Domain and range
sin and cos take every real number and return values in [-1, 1]. tan takes every real number except odd multiples of pi/2 and returns all real numbers.
4. Sum and difference formulas
sin(A + B) = sinA cosB + cosA sinB; cos(A + B) = cosA cosB - sinA sinB; tan(A + B) = (tanA + tanB)/(1 - tanA tanB). They give exact values for 75 degrees, 15 degrees and friends.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Convert degrees to radians
Choose the method: Multiply by pi/180.
EZT practice question
Convert 75 degrees to radians.
Show the worked solution
- 75 degrees = 75 x pi/180 rad.
- 75/180 = 5/12.
Answer: 5pi/12 rad.
Check: 5pi/12 x 180/pi = 75 - back where we started.
Watch for this: Do not divide by 360; the conversion factor is pi/180.
Now try it yourself
Convert 105 degrees to radians.
Check your answer
7pi/12 rad.
105/180 = 7/12.
Convert radians to degrees
Choose the method: Multiply by 180/pi.
EZT practice question
Convert 2pi/9 rad to degrees. Also, how many degrees is 1 radian?
Show the worked solution
- 2pi/9 x 180/pi = 2 x 20 = 40 degrees.
- 1 rad = 180/pi, about 57.30 degrees.
Answer: 40 degrees; 1 radian is about 57.30 degrees.
Check: pi rad = 180 degrees, so 2pi/9 must be well under 90 degrees - 40 fits.
Watch for this: Do not leave the calculator in radian mode when checking degree answers.
Now try it yourself
Convert 5pi/6 rad to degrees.
Check your answer
150 degrees.
5pi/6 x 180/pi = 5 x 30 = 150.
Use l = r theta
Choose the method: Theta must be in radians.
EZT practice question
A circle has radius 6 cm. Find the arc length subtended by an angle of pi/3 at the centre.
Show the worked solution
- l = r theta with theta in radians.
- l = 6 x pi/3.
Answer: l = 2pi cm.
Check: pi/3 is one sixth of a full circle; the circumference 12pi divided by 6 is 2pi.
Watch for this: Do not plug 60 into l = r theta; convert degrees to radians first.
Now try it yourself
Same circle, angle pi/6 - arc length?
Check your answer
pi cm.
l = 6 x pi/6 = pi.
Read signs by quadrant
Choose the method: All, sin, tan, cos - in order from the first quadrant.
EZT practice question
In which quadrants are sin, cos and tan each positive?
Show the worked solution
- First quadrant: all three positive.
- Second: only sin. Third: only tan. Fourth: only cos.
Answer: sin positive in quadrants one and two; cos in one and four; tan in one and three.
Check: At 120 degrees (second quadrant) sin is positive and cos negative - consistent.
Watch for this: Do not assume every ratio is positive in the first two quadrants; only sin survives the second.
Now try it yourself
What is the sign of tan 210 degrees?
Check your answer
Positive.
210 degrees sits in the third quadrant, where tan is positive.
State domain and range
Choose the method: Memorise the table from the chapter.
EZT practice question
Give the domain and range of sin x, cos x and tan x.
Show the worked solution
- sin and cos: domain all real numbers, range [-1, 1].
- tan: domain all reals except odd multiples of pi/2, range all real numbers.
Answer: sin and cos: R to [-1, 1]; tan: R minus the odd multiples of pi/2, onto all of R.
Check: tan blows up exactly where cos is zero - the odd multiples of pi/2.
Watch for this: Do not give tan a domain of all real numbers; it is undefined at pi/2.
Now try it yourself
What is the range of cos x?
Check your answer
[-1, 1].
The x-coordinate on the unit circle never leaves that interval.
Find sin 75 exactly
Choose the method: Write 75 as 45 + 30 and use the sum formula.
EZT practice question
Find the exact value of sin 75 degrees.
Show the worked solution
- sin(45 + 30) = sin45 cos30 + cos45 sin30.
- = (1/sqrt2)(sqrt3/2) + (1/sqrt2)(1/2) = (sqrt3 + 1)/(2sqrt2).
- Rationalising gives (sqrt6 + sqrt2)/4.
Answer: (sqrt6 + sqrt2)/4, about 0.9659.
Check: 75 degrees is steep, so its sine should be close to 1 - 0.9659 fits.
Watch for this: Do not write sin45 + sin30; the sum formula is not distributive.
Now try it yourself
Find sin 15 degrees exactly.
Check your answer
(sqrt6 - sqrt2)/4.
sin(45 - 30) = sin45 cos30 - cos45 sin30.
Find cos 75 and tan 75 exactly
Choose the method: cos(A + B) carries the minus sign; tan follows by division or its own formula.
EZT practice question
Find exact values of cos 75 degrees and tan 75 degrees.
Show the worked solution
- cos(45 + 30) = cos45 cos30 - sin45 sin30 = (sqrt6 - sqrt2)/4.
- tan 75 = sin75/cos75 = (sqrt6 + sqrt2)/(sqrt6 - sqrt2), which simplifies to 2 + sqrt3.
Answer: cos 75 = (sqrt6 - sqrt2)/4; tan 75 = 2 + sqrt3.
Check: cos 75 is small (about 0.2588) and tan 75 large (about 3.73) - consistent for a steep angle.
Watch for this: Do not carry a plus into cos(A + B); it is cosA cosB - sinA sinB.
Now try it yourself
Find cos 15 degrees exactly.
Check your answer
(sqrt6 + sqrt2)/4.
cos(45 - 30) = cos45 cos30 + sin45 sin30 - same value as sin 75.
Keep the sum and difference signs straight
Choose the method: sin keeps the sign; cos flips it.
EZT practice question
Write down sin(A - B) and cos(A - B).
Show the worked solution
- sin(A - B) = sinA cosB - cosA sinB.
- cos(A - B) = cosA cosB + sinA sinB.
Answer: sin(A - B) = sinA cosB - cosA sinB; cos(A - B) = cosA cosB + sinA sinB.
Check: Put B = A: sin 0 = 0 and cos 0 = cos^2 A + sin^2 A = 1 - both correct.
Watch for this: The classic slip: cos(A + B) already has the minus, so cos(A - B) takes the plus.
Now try it yourself
Write tan(A - B).
Check your answer
(tanA - tanB)/(1 + tanA tanB).
Replace B by -B in the sum formula and use tan(-B) = -tanB.
Try a mixed set
Choose a method or explanation before opening each answer.
1. pi radians in degrees?
Show answer and reason
180 degrees.
The whole conversion system hangs on this one fact.
2. What unit does l = r theta need?
Show answer and reason
Radians.
The formula is derived from the radian definition of angle.
3. sin(A + B)?
Show answer and reason
sinA cosB + cosA sinB.
It produces exact values for angles like 75 degrees.
4. cos(A + B)?
Show answer and reason
cosA cosB - sinA sinB.
The sign flips - the most-tested detail in the chapter.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Convert 105 degrees to radians.
- Convert 5pi/6 rad to degrees.
- Find the exact value of sin 15 degrees.
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Questions about this practice page
- Why do we need radians?
- Radian measure ties the angle directly to arc length (l = r theta) and makes calculus formulas clean; degrees are arbitrary divisions of the circle.
- What are the domain and range of sin and cos?
- Both take all real numbers and return values in [-1, 1].
- How do I remember the sum formulas?
- sin(A + B) keeps the plus between terms; cos(A + B) flips it to a minus. Test them with A = B = 0 when in doubt.
- Is sin 75 degrees the same as cos 15 degrees?
- Yes - both equal (sqrt6 + sqrt2)/4, because 75 and 15 are complementary angles.
- Are these the NCERT exercise questions for Trigonometric Functions (Class 11)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.