Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Define sin θ and cos θ for a right-angled triangle. sin θ = opposite sidehypotenusehypotenuseopposite side, cos θ = adjacent sidehypotenusehypotenuseadjacent side

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° = 3213

Perfect! This is a standard trigonometric value.

(5) Write the reciprocal of sin θ. Reciprocal of sin θ = θ

Excellent! Cosecant is the reciprocal of sine.

(6) What is the value of sec 90°? sec 90° = undefined01

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: (longest side), side (opposite to angle A), side (next to angle A)

Perfect! These are the three sides used in trigonometric ratios.

(8) If tan θ = 1, what is the value of sin2θ + cos2θ? sin2θ + cos2θ =

Excellent! This is the fundamental trigonometric identity.

Short Answer Questions (2 Marks Each)

(1) Evaluate: sin 60° × cos 30° + sin 30° × cos 60°

sin 60° = 3222, cos 30° = 3222

Answer =

Perfect! This actually equals sin(60° + 30°) = sin 90° = 1.

(2) If cos θ = 45 and θ is acute, find sin θ and tan θ.

sin θ =

tan θ =

Excellent! Used the Pythagorean identity systematically.

(3) Using the identity sin2θ + cos2θ = 1, find sin θ if cos θ = 0.6 sin θ = ±0.80.8-0.8

Perfect! Don't forget the ± sign when taking square roots.

(4) Express cot θ in terms of sin θ and cos θ. cot θ = cosθsinθsinθcosθ

Excellent! Cotangent is the reciprocal of tangent.

(5) Prove: tan2θ + 1 = sec2θ

(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 = 5353 m

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 3 = 1.732). d = m

Perfect! Used the relationship between depression and elevation angles.

Long Answer Questions (4 Marks Each)

(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 3 = 1.732) h = m

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 23 m long. Find the angle of elevation of the Sun. θ = °

Excellent! Recognized the standard angle value.

(4) Show that: sin230°+cos260°tan245°+cot245° = 12

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) 12 (d) 32

Correct! sin 0° = 0 is a standard trigonometric value.

(2) The value of tan 60° is:

(a) 1 (b) 3 (c) 0 (d) 13

Correct! tan 60° = 3 is a standard angle value.

(3) The identity sin2θ + cos2θ = ?

(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) 3

Correct! sec 0° = 1cos0° = 11 = 1.

(5) cot θ is equal to:

(a) 1tanθ (b) tan θ (c) sinθcosθ (d) 1cosθ

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° = sin90°cos90° = 10, which is undefined.

(7) In a right triangle, tan θ = oppositeadjacent means:

(a) PerpendicularBase (b) HypotenuseBase (c) BasePerpendicular (d) None

Correct! In a right triangle, opposite side is perpendicular and adjacent side is base.

(8) sin 30° × cos 60° =

(a) 12 (b) 14 (c) 34 (d) 34

Correct! sin 30° = 12, cos 60° = 12, so 12 × 12 = 14.

(9) If sin θ = 35, then cos θ =

(a) 45 (b) 54 (c) 125 (d) Not defined

Correct! Using sin2θ + cos2θ = 1: cos2θ = 1 - 352 = 1625, so cos θ = 45.

(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:

Basic Trigonometry Quiz

🎉 You Did It! What You've Learned:

By completing this worksheet, you now have a solid understanding of:

(1) Basic Definitions: Understanding sin, cos, tan and their reciprocals

(2) Standard Angle Values: Memorizing values for 0°, 30°, 45°, 60°, 90°

(3) Fundamental Identity: sin2θ + cos2θ = 1 and its applications

(4) Reciprocal Relationships: cosec, sec, cot as reciprocals of basic ratios

(5) Right Triangle Applications: Using ratios to solve practical problems

(6) Identity Proofs: Basic algebraic manipulation of trigonometric expressions

(7) Problem-solving Skills: Applying trigonometry to height-distance problems

(8) Foundation Building: Essential skills for advanced trigonometry

Excellent work building a strong foundation in basic trigonometry!