Introduction to Trigonometry quiz

If sin A = 3/4, then cos A is:

The value of tan 45 degrees is:

The value of (2 tan 30)/(1 + tan^2 30) is:

sin 2A = 2 sin A is true when A equals:

The value of sin^2 60 + cos^2 60 is:

Which of the following is not defined?

9 sec^2 A - 9 tan^2 A is equal to:

(1 + tan^2 A)/(1 + cot^2 A) is equal to:

If cos A = 4/5, the value of tan A is:

The value of sin 30 cos 60 + cos 30 sin 60 is:

If sin A = 3/4, calculate cos A and tan A. (2 marks)

If angles A and B are acute angles such that cos A = cos B, show that angle A = angle B. (2 marks)

Evaluate 2 tan^2 45 + cos^2 30 - sin^2 60. (2 marks)

Show that (1 + tan^2 A)/(1 + cot^2 A) = tan^2 A. (2 marks)

Prove that (sec A + tan A)(1 - sin A) = cos A. (2 marks)

If sin (A - B) = 1/2 and cos (A + B) = 1/2, with 0 < A + B <= 90 degrees and A > B, find A and B. (2 marks)

Express sec A in terms of cot A. (2 marks)

Prove that (1 + sec A)/sec A = sin^2 A/(1 - cos A). (2 marks)

Given sec theta = 13/12, calculate all the other trigonometric ratios. (2 marks)

If 3 cot A = 4, check whether (1 - tan^2 A)/(1 + tan^2 A) = cos^2 A - sin^2 A. (2 marks)

In triangle ABC, right-angled at B, AB = 24 cm and BC = 7 cm. Determine (i) sin A and cos A (ii) sin C and cos C (iii) verify that sin^2 A + cos^2 A = 1. (3 marks)

If cot theta = 7/8, evaluate (i) ((1 + sin theta)(1 - sin theta))/((1 + cos theta)(1 - cos theta)) (ii) cot^2 theta. (3 marks)

In triangle PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine angle QPR and angle PRQ. (3 marks)

Evaluate (sin 30 + tan 45 - cosec 60)/(sec 30 + cos 60 + cot 45). (3 marks)

A ladder 10 m long leans against a wall and makes an angle of 60 degrees with the ground. Find the distance of the foot of the ladder from the wall and the height at which the ladder touches the wall. (Use sqrt(3) = 1.73) (3 marks)

Read the passage and answer the questions. A ramp for wheelchair users is built at the entrance of a school. The ramp rises 1 m over a horizontal distance of sqrt(3) m, forming a right triangle with the ground and the vertical wall of the platform. (i) Find the length of the sloping surface of the ramp. (ii) Find the tan of the angle of slope of the ramp and hence the angle it makes with the ground. (iii) Find sin and cos of this angle from the sides of the triangle. (5 marks)

Read the passage and answer the questions. A kite string is tied to a peg on the ground. When the string is fully stretched, the kite is at a height of 30 m and the horizontal distance between the peg and the point directly below the kite is 40 m. (i) Find the length of the string. (ii) Find sin theta, cos theta and tan theta, where theta is the angle the string makes with the ground. (iii) Verify that 1 + tan^2 theta = sec^2 theta for this angle. (5 marks)

Read the passage and answer the questions. An electrician wants to repair a fault on a pole of height 5 m. She needs to reach a point 1.3 m below the top of the pole. She uses a ladder inclined at an angle of 60 degrees to the horizontal. (i) At what height must the top of the ladder rest on the pole? (ii) Write the trigonometric ratio that connects this height with the length of the ladder. (iii) Find the length of the ladder needed. (Use sqrt(3) = 1.73) (5 marks)

Read the passage and answer the questions. In a geometry lab, students cut a right triangle ABC from cardboard, right-angled at B, with AB = 12 cm and AC = 13 cm. They are asked to find the ratios for angle A and angle C. (i) Find BC. (ii) Write sin A, cos A and tan A. (iii) Show that sin A = cos C and explain why this is so in terms of the sides. (5 marks)

Read the passage and answer the questions. A student claims that because sin 30 = 1/2 and sin 60 = sqrt(3)/2, sin (30 + 60) should be (1 + sqrt(3))/2. Her friend says this is wrong. (i) Find the actual value of sin 90 degrees. (ii) Find (1 + sqrt(3))/2 approximately and explain why it cannot be the sine of any angle. (iii) Does sin (A + B) = sin A + sin B in general? Justify with one more pair of angles. (5 marks)

Draw an equilateral triangle and an isosceles right triangle with suitable labelling, and use them to derive the values of all six trigonometric ratios of 30, 45 and 60 degrees. Present the values for 0, 30, 45, 60 and 90 degrees in a neatly written list, stating which ratios are not defined. (6 marks)

Prove the identity sin^2 A + cos^2 A = 1 using a right triangle ABC, right-angled at B, drawing the figure. Hence prove that 1 + tan^2 A = sec^2 A and 1 + cot^2 A = cosec^2 A, and state the values of A for which each identity is valid. (6 marks)

Prove that (cos A - sin A + 1)/(cos A + sin A - 1) = cosec A + cot A, using the identity cosec^2 A = 1 + cot^2 A. (6 marks)

If tan A = 1/sqrt(3), draw a suitable right triangle and find all other trigonometric ratios of A. Find the angle A and evaluate sin A cos C + cos A sin C, where C is the third angle of the triangle with B = 90 degrees. (6 marks)

Prove that (tan theta)/(1 - cot theta) + (cot theta)/(1 - tan theta) = 1 + sec theta cosec theta. Draw a right triangle to illustrate theta and explain why the identity does not hold when theta = 45 degrees. (6 marks)