Easy Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define sin θ and cos θ for a right-angled triangle. sin θ =
Perfect! These are the fundamental trigonometric ratios.
(2) Write the value of tan 45°. tan 45° =
Correct! This is one of the standard angle values.
(3) If sin θ = 0, then what is the value of θ? θ =
Excellent! sin θ = 0 when θ is a multiple of
(4) Find cos 30°. cos 30° =
Perfect! This is a standard trigonometric value.
(5) Write the reciprocal of sin θ. Reciprocal of sin θ =
Excellent! Cosecant is the reciprocal of sine.
(6) What is the value of sec 90°? sec 90° =
Correct! Division by zero makes sec 90° undefined.
(7) Name the sides of a right triangle with respect to angle A. The three sides are:
Perfect! These are the three sides used in trigonometric ratios.
(8) If tan θ = 1, what is the value of
Excellent! This is the fundamental trigonometric identity.
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation, in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) Evaluate: sin 60° × cos 30° + sin 30° × cos 60°
sin 60° =
Answer =
Perfect! This actually equals sin(60° + 30°) = sin 90° = 1.
(2) If cos θ =
sin θ =
tan θ =
Excellent! Used the Pythagorean identity systematically.
(3) Using the identity
Perfect! Don't forget the ± sign when taking square roots.
(4) Express cot θ in terms of sin θ and cos θ. cot θ =
Excellent! Cotangent is the reciprocal of tangent.
(5) Prove:
(6) If a ladder of length 10 m makes an angle of 60° with the ground, find the height it reaches on the wall. h =
Excellent application of sine ratio!
(7) From the top of a building 20 m high, the angle of depression of a car is 30°. Find the distance of the car from the building (use
Perfect! Used the relationship between depression and elevation angles.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) A man is standing 40 m away from a tower. The angle of elevation of the top of the tower is 60°. Find the height of the tower. (Use
Excellent! Complete solution with proper steps and numerical answer.
(2) In a triangle ABC, right-angled at B, if AB = 5 cm and BC = 12 cm, find all the trigonometric ratios of angle C.
sin C =
cos C =
tan C =
cosec C =
sec C =
cot C =
Perfect! Found all six trigonometric ratios systematically.
(3) A vertical pole 6 m high casts a shadow
Excellent! Recognized the standard angle value.
(4) Show that:
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The value of sin 0° is:
(a) 1 (b) 0 (c)
Correct! sin 0° = 0 is a standard trigonometric value.
(2) The value of tan 60° is:
(a) 1 (b)
Correct! tan 60° =
(3) The identity
(a) 0 (b) 1 (c) 2 (d) Depends on θ
Correct! This is the fundamental trigonometric identity, always equals 1.
(4) The value of sec 0° is:
(a) 1 (b) 0 (c) Not defined (d)
Correct! sec 0° =
(5) cot θ is equal to:
(a)
Correct! Cotangent is the reciprocal of tangent.
(6) Which of the following is not defined?
(a) sin 0° (b) cos 0° (c) tan 90° (d) cot 0°
Correct! tan 90° =
(7) In a right triangle, tan θ =
(a)
Correct! In a right triangle, opposite side is perpendicular and adjacent side is base.
(8) sin 30° × cos 60° =
(a)
Correct! sin 30° =
(9) If sin θ =
(a)
Correct! Using
(10) Which of the following is true?
(a) sin 90° = 0 (b) cos 90° = 1 (c) tan 45° = 1 (d) sec 0° = 0
Correct! tan 45° = 1 is a standard trigonometric value.
Basic Trigonometry Challenge
Determine whether these statements about basic trigonometry are True or False: