Trigonometry -30-05-2025

Trigonometry

By WINCENTRE CP1

Multiple Choice

What is the value of sin 30°?

• 1
• 0
• ½
• √3/2

Multiple Choice

If tan A = 1, then angle A is:

• 0°
• 30°
• 45°
• 90°

Multiple Choice

What is the value of sin 30°?

• 1
• 0
• ½
• √3/2

Multiple Choice

If tan A = 1, then angle A is:

• 0°
• 30°
• 45°
• 90°

Multiple Choice

What is the value of cos 0°?

• 1
• 0
• ½
• Undefined

Explanation Slide...

cos 0° = 1 from trigonometric values.

Multiple Choice

If sin A = 3/5, then cos A = ?

• 4/5
• 3/4
• √7/5
• √16/5

Explanation Slide...

cos A = √(1 - sin²A) = √(1 - 9/25) = √(16/25) = 4/5

Multiple Choice

What is the value of tan 60°?

• 1
• √3
• 0
• 1/√3

Multiple Choice

sin²A + cos²A = ?

• 0
• 1
• 2
• Depends on A

Multiple Choice

What is the value of cot 45°?

• 1
• 0
• √3
• 1/√3

Multiple Choice

sec A is the reciprocal of:

• sin A
• cos A
• tan A
• cot A

Multiple Choice

Which of the following is undefined?

• tan 90°
• sin 90°
• cos 90°
• tan 0°

Multiple Choice

In a right triangle, if one angle is 60°, the other non-right angle is:

• 30°
• 45°
• 60°
• 90°

Explanation Slide...

Sum of angles in a triangle = 180°. Right angle = 90°, so remaining = 90°. Hence, other angle = 30°.

Multiple Choice

What is the value of sin(A + B)?

• sin A + sin B
• sin A cos B + cos A sin B
• cos A cos B - sin A sin B
• cos A - cos B

Multiple Choice

What is the value of cos(A + B)?

• cos A + cos B
• cos A cos B - sin A sin B
• cos A cos B + sin A sin B
• sin A sin B - cos A cos B

Multiple Choice

If sin x = 0.8, what is cos x?

• 0.6
• 0.5
• 0.75
• 0.4

Explanation Slide...

cos x = √(1 - sin²x) = √(1 - 0.64) = √0.36 = 0.6

Multiple Choice

Which of the following is/are equal to 1?

• sin 90°
• cos 0°
• tan 45°
• All of the above

Explanation Slide...

All values are standard trigonometric identities: sin 90° = 1, cos 0° = 1, tan 45° = 1

Multiple Choice

From a 50 m high lighthouse, angle of depression to a boat is 30°. Distance from base?

• 50 m
• 50√3 m
• 25 m
• 100 m

Explanation Slide...

Using tangent formulas and geometry, the difference in heights gives 6.6 m.

Explanation Slide...

Distance = height / tan(30°) = 50 / (1/√3) = 50√3.

Multiple Choice

A 12 m high tree casts a 12√3 m shadow. Find angle of elevation of sun.

• 30°
• 45°
• 60°
• 90°

Explanation Slide...

tan θ = 12 / 12√3 = 1/√3 → θ = 30°

Multiple Choice

Two men see a tower from opposite sides with angles 45° & 30°, tower height = 80 m. Distance between them?

• 212.12 m
• 218.13 m
• 21.813 m
• 21.212 m

Explanation Slide...

Using tan(θ) = h/d for both and adding distances gives ~218.13 m.

Multiple Choice

sin(180° − φ) is equal to:

• sin φ
• cos φ
• cosec φ
• tan φ

Explanation Slide...

sin(180° − φ) = sin φ (sine is positive in second quadrant).

Multiple Choice

If sin A = 0.6, what is cos A?

• 0.8
• 0.5
• 0.75
• 1

Explanation Slide...

cos A = √(1 – sin²A) = √(1 – 0.36) = 0.8

Multiple Choice

Which of the following is equal to cos 30°?

• sin 60°
• sin 30°
• tan 60°
• cos 60°

Explanation Slide...

cos 30° = √3/2, which is also sin 60°.

Multiple Choice

Which identity is correct?

• sin(90° − θ) = tan θ
• cos(90° − θ) = sin θ
• tan(90° − θ) = cos θ
• sec(90° − θ) = cot θ

Explanation Slide...

cos(90° − θ) = sin θ is a standard complementary identity.

Multiple Choice

The value of 36⁰ in radian is

• π/4

• π/5

• π/6

• π/2

Multiple Choice

A 20 m high tower has angles of elevation 60° to the bottom and 30° to top of a pole. Height of pole?

• 5 m
• 6.6 m
• 13.3 m
• 15.2 m