Introduction to Trigonometry Worksheet-1

 ~Anshul Gurjar

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1. In ∆ ABC, positioned right to B, AB = 24 cm, BC = 7 cm. The value of tan C is:

(a) 12/7

(b) 24/7

(c) 20/7

(d) 7/24

Answer: (b)

Definition: AB = 24cm and BC = 7cm

Tan C = Different side / side side

Tan C = 24/7

2. (Sin 30 ° + cos 60 °) - (sin 60 ° + cos 30 °) equals:

(a) 0

(b) 1 + 2√3

(c) 1-√3

(d) 1 + √3

Answer: c

Definition: sin 30 ° = ½, sin 60 ° = √3 / 2, cos 30 ° = √3 / 2 and cos 60 ° = ½

To set these values, we find:

(½ + ½) - (√3 / 2 + √3 / 2)

= 1-√3

3. The temperature of 60 ° / cot 30 ° is equal to:

(a) 0

(b) 1

(c) 2

(d) 3

Answer: b

Description: tan 60 ° = √3 and 30 ° = √3

Therefore, tan 60 ° / 30 ° = = √3 / =3 = 1

4. 1-cos2A equals:

(a) sin2A

(b) tan2A

(c) 1-sin2A

(d) sec2A

Answer: a

Definition: We know, by trigonometry,

sin2A + cos2A = 1

1-cos2A = sin2A

5. Sin (90 ° - A) and cos A are:

(a) The exception

(b) Same

(c) Not related

(d) None of the above

Answer: b

Definition: With trigonometry identity.

Sin (90 ° -A) = cos A [comes in the first place of the unit circle]

6. If cos X = ⅔ then tan X is equal to:

(a) 5/2

(b) √ (5/2)

(c) /5 / 2

(d) 2 / √5

Answer: (c)

Definition: By identifying trigonometry, we know:

1 + tan2X = sec2X

And sec X = 1 / cos X = 1 / (⅔) = 3/2

Therefore,

1 + tan2X = (3/2) 2 = 9/4

tan2X = 9 / 4-1 = 5/4

Tan X = /5 / 2

7. If cos X = a / b, sin X is equal to:

(a) b2-a2 / b

(b) b-a / b

(c) √ (b2-a2) / b

(d) √ (b-a) / b

Answer: (c)

Definition: cos X = a / b

With trigonometry ownership, we know that:

sin2X + cos2X = 1

sin2X = 1-cos2X = 1- (a / b) 2

Sin X = √ (b2-a2) / b

8. The value of sin 60 ° cos 30 ° + sin 30 ° cos 60 ° is:

(a) 0

(b) 1

(c) 2

(d) 4

Answer: b

Definition: sin 60 ° = √3 / 2, sin 30 ° = ½, cos 60 ° = ½ and cos 30 ° = √3 / 2

Therefore,

√3 / 2 x √3 / 2 + ½ x ½

= 3/4 + 1/4

= 1

9. 2tan 30 ° / 1 + tan230 ° =

(a) Sin 60 °

(b) ICos 60 °

(c) Tan 60 °

(d) Sin 60 °

Answer: a

Specification: tan 30 ° = 1 / √3

To set the amount we receive;

2 (1 / √3) / 1 + (1 / √3) 2 = (2 / √3) / 4/3 = 6 / 4√3 = √3 / 2 = sin 60 °

10. sin 2A = 2 sin A is true when A =

(a) 30 °

(b) 45 °

(c) 0 °

(d) 60 °

Answer: (c)

Definition: sin 2A = sin 0 ° = 0

2sin A = 2sin 0 ° = 0