Trigonometry (Maxima and Minima)

Hello guys, How are you? I hope are you fine and well. So in this page we discussed important questions related to Trigonometry. In Trigonometry, we discussed where the value of some equality lies....

So, let's start the series:

First question is

1. Find the maximum and minimum value of 27sinθ + 36 cosθ.

(A) 45, -45
(B) 45, -50
(C) 50, -45
(D) 50, -50

【video solution】

2. Find the maximum and minimum value of 25sinθ × 125 cosθ.

(A) 5^√13, (1/5)^√13

(B) 5^4, (1/5)^4

(C) 5^√12, (1/5)^√12

(D) 5^3, (1/5)^3


3. Find the maximum value of 12sinθcosθ + 1 -2sin²Î¸ + 8.

(A) 8 + √35

(B) 8 + √37

(C) 7 + √30

(D) 7 + √35


4. Find the maximum value of 48sin²Î¸ + 32cos²Î¸.

(A) 58

(B) 40

(C) 32

(D) 48


5. 27sec²Î¸ + 20tan²Î¸. Find the minimum value.

(A) 47

(B) 27

(C) 20

(D) 07


6. Find the minimum value of 3^cotθ × 9^cot²Î¸ × 81^tan²Î¸ + 60.

(A) 3^√13

(B) 3^2√3

(C) 3^4√3

(D) 3^4


7. Find the maximum and minimum value of 10√2sinθcos(θ-Ï€/4) + 50

(A) 50 - √225 and 50 + √225

(B) √221 + 50 and -√221 + 50

(C) √220 + 50 and -√220 + 50

(D) √224 + 50 and -√224 + 50


8. Find the maximum and minimum value of sin¹²⁰θcos¹²⁰θ

(A) 1/2, 0

(B) (1/2)^120, 0

(C) 0, 2^120

(D) 0, (1/2)^120


9. Find the maximum and minimum value of sin¹⁶θ + cos¹⁰θ.

(A) 1, 9/256

(B) -1, 9/256

(C) 3, 11/256

(D) 1, 7/256


10. Find the minimum value of 20sin²Î¸ + 78cosec²Î¸.

(A) 20

(B) 98

(C) 78

(D) 100


11. Find the minimum value of 36sin²Î¸ + 8cosec²Î¸.

(A) 25

(B) 24√3

(C) 24

(D) 24√2


12. Find the minimum value of 64sec²Î¸ + 36cosec²Î¸.

(A) 197

(B) 200

(C) 196

(D) 198


13. Find the maximum value of 1/(sin²Î¸ + 3sinθcosθ + 5cos²Î¸)

(A) 4

(B) 2

(C) 6 

(D) 5


14. Find the maximum value of 3cos²x + 2sinx + 1.

(A) 13/3

(B) 8

(C) 7

(D) 16/3


15. Find the maximum and minimum value of sin²(120-θ) + sin²(120+θ)

(A) 3/2, 1/2

(B) 3/2, -1/2

(C) 1/2, -3/2

(D) 1/2, -1


16. Find the minimum value of 3cos²Î¸ + 12cosθ - 3

(A) -10

(B) 10

(C) 12

(D) -12


17. Find the minimum value of 4sin²Î¸ + 9cos²a + 9cosec²Î¸ + 4sec²a + 10

(A) 35

(B) -35

(C) 30

(D) 25


18. If A + B = 90° the maximum value of cosAcosB is

(A) 1/4

(B) 1/2

(C) 1/3

(D) 1/6


19. sin3θ + cos3θ is the maximum when 0 is.

(A) 45°

(B) 60°

(C) 15°

(D) 30°


20. Find the minimum value of 16sin²Î¸+ 9cot²Î¸ + 3.

(A) 16

(B) 18

(C) 20

(D) 24


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