Trig Identities Qs
Trig Identities Qs
Trig Identities Qs
5
1. If A is an obtuse angle in a triangle and sin A = 13 , calculate the exact value of sin 2A.
Working:
Answer:
......................................................................
(Total 4 marks)
2
2. (a) Express 2 cos x + sin x in terms of sin x only.
2
(b) Solve the equation 2 cos x + sin x = 2 for x in the interval 0 x , giving your answers exactly.
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(Total 4 marks)
IB Questionbank Maths SL 1
2 2
3. (a) Write the expression 3 sin x + 4 cos x in the form a cos x + b cos x + c.
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(Total 4 marks)
2
4. Consider the trigonometric equation 2 sin x = 1 + cos x.
2
(a) Write this equation in the form f (x) = 0, where f (x) = a cos x + b cos x + c,
and a, b, c .
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(c) ..................................................................
(Total 6 marks)
2
5. Solve the equation 2 cos x = sin 2x for 0 x , giving your answers in terms of .
IB Questionbank Maths SL 2
Working:
Answer:
..
(Total 6 marks)
6. The function f is defined by f : x 30 sin 3x cos 3x, 0 x 3 .
(a) Write down an expression for f (x) in the form a sin 6x, where a is an integer.
1
7. Given that sin x = 3 , where x is an acute angle, find the exact value of
(a) cos x;
Working:
Answers:
(a) ..................................................................
(b) ..................................................................
(Total 6 marks)
2
8. Let f (x) = a (x 4) + 8.
IB Questionbank Maths SL 3
(a) Write down the coordinates of the vertex of the curve of f.
9. The following diagram shows a triangle ABC, where ACB is 90, AB = 3, AC = 2 and BAC is .
5
(a) Show that sin = 3 .
4 5
(b) Show that sin 2 = 9 .
3
x
11. The straight line with equation y = 4 makes an acute angle with the x-axis.
(i) sin 2;
(ii) cos 2.
(6)
(Total 7 marks)
IB Questionbank Maths SL 4
2
12. (a) Show that 4 cos 2 + 5 sin = 2 sin + 5 sin + 3.
(2)
3 3
13. Let f(x) = sin x + cos x tan x, 2 < x < .
2 4 5
(b) Let sin x = 3 . Show that f(2x) = 9 .
(5)
(Total 7 marks)
2 2
14. Solve cos 2x 3 cos x 3 cos x = sin x, for 0 x 2.
(Total 7 marks)
2
15. (a) Consider the equation 4x + kx + 1 = 0. For what values of k does this equation have two equal
roots?
(3)
2
(b) Show that this function may be written as f ( ) = 4 cos + 4 cos + 1.
(1)
(d) Given that f ( ) = c is satisfied by only three values of , find the value of c.
(2)
(Total 11 marks)
IB Questionbank Maths SL 5