In worksheet on evaluation using trigonometric ratios of complementary angles we will solve various types of practice questions on trigonometric ratios of complementary angles. Here you will get 11 different types of questions on evaluation using trigonometric ratios of complementary angles.
1. If angle A of the ∆ ABC is complementary to 20° and angle B is complementary to \(\frac{2π}{9}\); find the angle C.
2. Evaluate without using trigonometric table:
(i) \(\frac{cos 80°}{sin 10°}\)
(ii) \(\sqrt{5}\) ∙ \(\frac{sin 18°}{cos 72°}\)
(iii) \(\frac{sin 15°}{cos 75°}\)
(iv) \(\frac{sec 20°}{csc 70°}\)
3. Evaluate without using trigonometric table:
(i) sin 54° - cos 36°
(ii) tan 10° - cot 72°
(iii) csc 12.5° – sec 77.5°
4. If the csc of an angle complementary to A be \(\frac{2}{\sqrt{3}}\), find tan A.
5. Evaluate without using trigonometric table:
(i) tan 63° tan 27°
(ii) cos 13° csc 77°
(iii) sin 40° sec 50°
(iv) (cos 15° - cos 75°) : (sin 75° - sin 15°)
(v) \(\frac{sin 80°}{cos 10°}\) + sin 59° sec 31°
6. Evaluate without using trigonometric table:
(i) sin 10° cos 80° + cos 10° sin 80°
(ii) cos 65° cos 25° - sin 65° sin 25°
(iii) sec 37° csc 53° - tan 37° cot 53°
(iv) 3 cos 80° ∙ csc 10° + 2 cos 59° ∙ csc 31°
7. (a) If sin 43° = m, find the value of
(i) cos 47°
(ii) sec 47°
(iii) tan 47°
(b) If sec 36° = a, find the value of tan 54°.
(c) If cot 12° = x, find the value of sec 78° + tan 78°.
8. Find the value of
(i) cos^{2} 18° + cos^{2} 36° + cos^{2} 54° + cos^{2} 72° + cos^{2} 90°
(ii) tan 10° tan 20° tan 40° tan 50° tan 70° tan 80°
9. Find the value of θ for each of the following equations:
(i) sin 4θ = cos θ
(ii) tan 3θ = cot θ
(iii) sin 3θ = cos 7θ
10. (i) If sin (2A) = cos 75°, find the smallest positive value of A.
(ii) If tanθ tan 40° = 1, find the value of θ.
(iii) If sin 22° csc (90° - θ) = 1, find θ.
(iv) If sec 5θ = csc 7θ, prove that θ = 7.5°.
11. (i) If cos 20° = m and cos 70° = n, find the value of m^{2} + n^{2}.
(ii) If sec 50° = a and cot 40° = b, find the value of a^{2} - b^{2}.
Answers on Worksheet on Evaluation using Trigonometric Ratios of Complementary Angles are given below to check the exact answers of the questions.
Answers:
1. 60° or \(\frac{π}{3}\)
2. (i) 1
(ii) \(\sqrt{5}\)
(iii) 1
(iv) 1
3. (i) 0
(ii) 0
(iii) 0
4. \(\frac{1}{\sqrt{3}}\)
5. (i) 1
(ii) 1
(iii) 1
(iv) 1
(v) 2
6. (i) 1
(ii) 0
(iii) 1
(iv) 5
7. (a) (i) m
(ii) \(\frac{1}{m}\)
(iii) \(\frac{\sqrt{1 – m^{2}}}{m}\)
(b) \(\frac{1}{\sqrt{a^{2} - 1}}\)
(c) \(\sqrt{1 + x^{2}}\) + x
8. (i) 2
(ii) 1
9. (i) 18°
(ii) 22.5°
(iii) 9°
10. (i) 7.5°
(ii) 50°
(iii) 68°
11. (i) 1
(ii) 1.
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