Introduction to Trigonometry

Which statement best summarizes the chapter "Introduction to Trigonometry"?

1. Trigonometry studies only circles.
2. Trigonometry introduces trigonometric ratios, standard angle values, reciprocal ratios, and identities that relate the sides and angles of right-angled triangles and help solve practical problems involving heights and distances.
3. Trigonometry deals only with algebraic equations.
4. Trigonometry has no practical applications.

Which trigonometric ratio equals sinθ/cosθ?

1. Cot θ
2. Tan θ
3. Sec θ
4. Cosec θ

Which ratio represents Hypotenuse/Opposite?

1. Sin θ
2. Cosec θ
3. Cos θ
4. Tan θ

If tan θ = 3/4, then cot θ equals:

1. 4/3
2. 3/4
3. 7/4
4. 1

The reciprocal of cos θ is:

1. Tan θ
2. Cot θ
3. Sec θ
4. Cosec θ

Which identity is always true?

1. sin²θ + cos²θ = 1
2. sinθ + cosθ = 1
3. tanθ = cosθ
4. sinθ = secθ

Which trigonometric ratio is the reciprocal of sin θ?

1. Sec θ
2. Cot θ
3. Cosec θ
4. Tan θ

The value of cos 60° is:

1. 0
2. 1/2
3. √3/2
4. 1

The value of sin 30° is:

1. 1
2. 1/2
3. √3/2
4. 0

The value of tan θ is:

1. Opposite/Hypotenuse
2. Adjacent/Hypotenuse
3. Opposite/Adjacent
4. Hypotenuse/Opposite

Which of the following represents cos θ?

1. Opposite/Hypotenuse
2. Adjacent/Hypotenuse
3. Hypotenuse/Adjacent
4. Opposite/Adjacent

In a right-angled triangle, sin θ is equal to:

1. Adjacent/Hypotenuse
2. Opposite/Hypotenuse
3. Hypotenuse/Opposite
4. Opposite/Adjacent

If (sin θ + cos θ)² = 1 + 2 sin θ cos θ, then sin θ cos θ is:

1. 0
2. 1
3. 1/2
4. −1/2

If cos θ = 0, then θ can be:

1. 0°
2. 30°
3. 60°
4. 90°

If sin θ = cos θ, then value of sin²θ + cos²θ is:

1. 0
2. 1
3. 2
4. 1/2

If tan θ = 3/4, find the value of (sin θ / cos θ)² + 1.

1. 1
2. 2
3. 25/16
4. 9/16

If sin θ = 1/2 and θ is acute, find sin θ + cos θ.

1. (1 + √3)/2
2. (√3 + 1)/2
3. √3/2
4. 1

If sin θ + cos θ = 1, then sin θ cos θ is:

1. 0
2. 1/2
3. 1
4. 2

If cos θ = 3/5, then tan θ is:

1. 3/4
2. 4/3
3. 5/4
4. 4/5

The value of (sec²θ − tan²θ) is:

1. 0
2. 1
3. −1
4. 2

If tan A = 1, then the value of sin A + cos A is:

1. 0
2. 1
3. √2/2
4. √2

If sin θ = 5/13, then cos θ is:

1. 12/13
2. 5/12
3. 13/12
4. 12/5

If 1 + tan²θ = sec²θ, then this identity is:

1. False
2. True
3. Sometimes true
4. Undefined

The value of (sin 30° + cos 60°) is:

1. 0
2. 1
3. 1/2
4. 2

If sin θ = cos θ, then θ is:

1. 30°
2. 45°
3. 60°
4. 90°

If tan θ = 12/5, then sin θ is:

1. 5/13
2. 12/13
3. 13/12
4. 12/5

If sin A = 3/5, then the value of cos A is:

1. 3/4
2. 4/5
3. 5/4
4. 2/5