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Advanced Trigonometry Problems

This document contains 13 math problems involving trigonometric functions such as sine, cosine, tangent, cotangent and secant. The problems cover a range of skills including expressing one trig function in terms of another, sketching graphs, solving equations, and finding values that satisfy trigonometric identities or equations.

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antonyluk
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124 views2 pages

Advanced Trigonometry Problems

This document contains 13 math problems involving trigonometric functions such as sine, cosine, tangent, cotangent and secant. The problems cover a range of skills including expressing one trig function in terms of another, sketching graphs, solving equations, and finding values that satisfy trigonometric identities or equations.

Uploaded by

antonyluk
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as RTF, PDF, TXT or read online on Scribd
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1 1 π

arctan   arctan  
4. (a) Show that  2  3 4 .

(2)

(b) Hence, or otherwise, find the value of arctan (2) + arctan (3).
(3)
(Total 5 marks)

5. A system of equations is given by

cos x + cos y = 1.2

sin x + sin y = 1.4.

(a) For each equation express y in terms of x.


(2)

(b) Hence solve the system for 0 < x < p, 0 < y < p.
(4)
(Total 6 marks)

7. (a) Sketch the curve f(x) = sin 2x, 0 ≤ x ≤ π.


(2)

(b) Hence sketch on a separate diagram the graph of g(x) = csc 2x, 0 ≤ x ≤ π, clearly stating
the coordinates of any local maximum or minimum points and the equations of any
asymptotes.
(5)

(c) Show that tan x + cot x ≡ 2 csc 2x.


(3)

(d) Hence or otherwise, find the coordinates of the local maximum and local minimum points
π
on the graph of y = tan 2x + cot 2x, 0 ≤ x ≤ 2 .
(5)

π
(e) Find the solution of the equation csc 2x = 1.5 tan x – 0.5, 0 ≤ x ≤ 2 .

1
(6)
(Total 21 marks)

8. Solve sin 2x = 2 cos x, 0 ≤ x ≤ π.

(Total 6 marks)

3
10. Given that tan 2θ = 4 , find the possible values of tan θ.
(Total 5 marks)

12. (a) If sin (x – α) = k sin (x + α) express tan x in terms of k and α.


(3)

1
(b) Hence find the values of x between 0° and 360° when k = 2 and α = 210°.
(6)
(Total 9 marks)

2
13. The angle θ satisfies the equation 2 tan θ – 5 sec θ – 10 = 0, where θ is in the second quadrant.
Find the value of sec θ.
(Total 6 marks)

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