Trigonometric Functions quiz

pi radians is equal to:

sin(-x) is equal to:

cos(pi - x) is equal to:

The range of cos x is:

sin 2x is equal to:

The period of tan x is:

The value of sec^2 x - tan^2 x is:

sin 30 cos 60 + cos 30 sin 60 (in degrees) equals:

In the third quadrant, the function that is positive is:

The value of cos(-1710 degrees) is:

Convert 6 radians into degree measure, using pi = 22/7. (2 marks)

Prove that sin^2(pi/6) + cos^2(pi/3) - tan^2(pi/4) = -1/2. (2 marks)

Find the value of tan 15 degrees. (2 marks)

Write sin 3x in terms of sin x. (2 marks)

Prove that cos 2x = cos^2 x - sin^2 x = 2cos^2 x - 1. (2 marks)

Explain why tan x is not defined at x = pi/2. (2 marks)

Find the value of cos 105 degrees. (2 marks)

Prove that (sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x. (2 marks)

Show that sin(pi + x) = -sin x. (2 marks)

Define a radian. (2 marks)

Find the radius of a circle in which a central angle of 60 degrees cuts off an arc of 37.4 cm. Use pi = 22/7. (3 marks)

Arcs of the same length in two circles subtend angles of 60 and 75 degrees at their centres. Find the ratio of their radii. (3 marks)

If sin x = 3/5 and cos y = -12/13, with x and y both in the second quadrant, find sin(x + y). (3 marks)

Prove that cos(pi/4 - x)cos(pi/4 - y) - sin(pi/4 - x)sin(pi/4 - y) = sin(x + y). (3 marks)

Find the value of sin 15 degrees cos 15 degrees. (3 marks)

Read the passage and answer the questions. The minute hand of a clock is 1.5 cm long. (i) Through how many degrees does it turn in 40 minutes? (ii) Convert this angle into radians. (iii) Find the distance moved by the tip of the hand in 40 minutes. (5 marks)

Read the passage and answer the questions. A pendulum 75 cm long swings so that its tip describes an arc of 10 cm. (i) Write the formula linking arc, radius and angle. (ii) Find the angle of swing in radians. (iii) Convert it into degrees, taking pi = 22/7. (5 marks)

Read the passage and answer the questions. A Ferris wheel has radius 10 m. After turning through angle theta from the lowest point, a seat is at height h = 10 - 10 cos(theta) above the lowest point. (i) Find h when theta = 60 degrees. (ii) Find h when theta = 90 degrees. (iii) Find h when theta = 180 degrees. (5 marks)

Read the passage and answer the questions. A surveyor uses the formula tan(A + B) = (tan A + tan B)/(1 - tan A tan B). Two angles have tan A = 1/2 and tan B = 1/3. (i) Find tan(A + B). (ii) Find A + B. (iii) What happens to the formula when tan A tan B = 1? (5 marks)

Read the passage and answer the questions. A student studies the graph of y = sin x. (i) State the maximum and minimum values. (ii) State the period. (iii) Find the values of x between 0 and 2pi where y = 0. (5 marks)

Explain degree and radian measure. Derive the relation between them and prove that l = r(theta) for arc length. (6 marks)

Define the six trigonometric functions using the unit circle. Explain their signs in each quadrant and their domains and ranges. (6 marks)

Prove the formula for sin(x + y). Hence derive formulas for sin(x - y) and sin 2x. (6 marks)

Prove that cos 3x = 4cos^3 x - 3cos x and tan 2x = 2tan x/(1 - tan^2 x). (6 marks)

Prove that (cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x. (6 marks)