Trigonometry

Written by Hassan Raza (Mathematics)

ECAT · Mathematics · 9 questions

Name: ____________________ Date: ____________

What is the value of sin 30 degrees + cos 60 degrees?
- A 1/2
- B 1
- C sqrt(3)
- D sqrt(3)/2
If sin A = 3/5 and A is acute, what is cos A?
- A 3/4
- B 5/3
- C 2/5
- D 4/5
If sin A = 3/5 and cos A = 4/5, what is sin 2A?
- A 12/25
- B 7/25
- C 24/25
- D 1
What is the period of the function tan x?
- A 4 pi
- B pi
- C 2 pi
- D pi / 2
What is the value of cos 60 degrees + cos 120 degrees?
- A 0
- B -1
- C 1
- D 1/2
How many solutions does sin x = 1/2 have in the interval from 0 to 2 pi?
- A 1
- B 3
- C 2
- D 4
A triangle has sides 3, 4 and 5. What is the angle opposite the side of length 5?
- A 90 degrees
- B 120 degrees
- C 45 degrees
- D 60 degrees
What is the area of a triangle with sides 7 and 8 and an included angle of 30 degrees?
- A 7 sqrt(3)
- B 14
- C 56
- D 28
Which expression equals cos(A + B)?
- A cos A cos B + sin A sin B
- B sin A sin B - cos A cos B
- C sin A cos B + cos A sin B
- D cos A cos B - sin A sin B

Answer key

1. B, 2. D, 3. C, 4. B, 5. A, 6. C, 7. A, 8. B, 9. D

Both sin 30 and cos 60 equal 1/2, so the sum is 1.
cos A = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.
sin 2A = 2 sin A cos A = 2 x (3/5) x (4/5) = 24/25.
The tangent function repeats every pi radians.
cos 60 = 1/2 and cos 120 = -1/2, so the sum is 0.
The solutions are x = pi/6 and x = 5 pi/6.
Since 3² + 4² = 5², the triangle is right-angled and the angle opposite the longest side is 90 degrees.
Area = 1/2 x 7 x 8 x sin 30 = 28 x 1/2 = 14.
The addition formula is cos(A + B) = cos A cos B - sin A sin B.