## Math : Trigonometry |

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Hide all answers View all answers Print Try the Quiz 1. For the figure given on the left, the value of sin C is• a / b • b / a • a / c • c / b • c / a Answer: c / b The sine of an angle is defined as Opposite Side / Hypotenuse. Now for angle C, the opposite side is c and the hypotenuse is b. Hence the correct answer is c/b. 2. From the figure given on the right, the value of sin A + cos A is • (b + c)/a • (a + b)/c • (a - b)/b • (a + c)/b • (a + b + c)/b Answer: (a + c)/b We know sin A = a/b, and cos A = c/b. Hence sin A + cos A = (a + c)/b.3. From the figure given on the left, the value of cos C is• a / b • b / a • c / a • c / b • b / c Answer: a / b We know that cos of any angle = Base/Hypotenuse. Now for the angle C, the base is a and hypotenuse is b. So cos C = a/b.
4. For the figure given on the right, which of the following relationships is true : • sin A = a / c
• cos A = b / c
• tan A = a / b
• cot A = c / a• sec A = b / a
Answer: cot A = c / aBy definition, cot A = 1 / tan A = c / a.5. From the figure given on the left, the value of cos C + sin A is• b/a + a/b • a/b + c/b • 2b/a • b/c + c/a • 2a/b Answer: 2a/b The value of cos C = a/b. Similarly the value of sin A = a/b. Hence cos C + sin A = 2a/b.6. Which of the following relationships is true:• sin A / cosec A = cot A
• cos A / sin A = sec A
• cosec A / sin A = cos A
• sin A / cos A = tan A• tan A / cot A = sin A
Answer: sin A / cos A = tan AThe expression sin A / cos A = tan A is a useful one to remember in trigonometry.7. tan A / sin A =• cosec A
• sin A
• cos A
• sec A• 1 / sin A
Answer: sec Atan A = sin A / cos A. Therefore tan A / sin A = 1 / cos A = sec A.8. (sin A / tan A) + cos A =• 2 sec A
• sec A
• 2 cos A• 2 cosec A
• 1 + cos A
Answer: 2 cos AWe know tan A = sin A / cos A. Therefore (sin A / tan A) + cos A = cos A + cos A = 2 cos A.9. cot A tan A =• sin A
• 1 • cos A
• sin A cos A
• 1/(sin A cos A)
Answer: 1 cot A = 1 / tan A. Hence cot A tan A = 1. Alternatively cot A = cos A/sin A and tan A= sin A/cos A. So cot A tan A = (cos A/sin A) (sin A/cos A) = 1.10. From the figure, the value of cosec A + cot A is• (a + b)/c • a/(b + c) • (b + c)/a • b/(a + c) • (a + c)/b Answer: (b + c)/a We know cosec A = b/a and cot A = c/a. Hence cosec A + cot A = (b + c)/a.11. Which of the following relationships is true:• sin A cot A = 1
• sin A + cosec A = 1
• sec A - cos A = 1
• sec A cot A = 1
• cos A sec A = 1Answer: cos A sec A = 1By definition, sec A = 1 / cos A. So cos A sec A = 1 is true.12. From the figure, the value of sin^{2} A + cos^{2} A is• a/b + c/b • b/a + c/b • 1 • (a/b + c/b) ^{2}
• (b/a + c/b) ^{2}
Answer: 1 This question is a bit tricky. We know sin A = a/b and cos A = c/b. So sin^{2} A + cos^{2} A = (a^{2} + c^{2}) / b^{2}. By Pythagoras Theorem, a^{2} + c^{2} = b^{2} for a right-angled triangle. Hence sin^{2} A + cos^{2} A = 1, which is a famous identity.13. From the figure, the value of cot C + cosec C is• (a + c)/b • (a + b)/c • (c + b)/a • a/c + c/b • c/a + b/c Answer: (a + b)/c cot C is Base/Opposite Side and cosec C is Hypotenuse/Opposite Side. From these definitions, the values of cot C and cosec C are given by a/c and b/c respectively. Hence the answer is (a + b)/c.14. cosec A / sec A =• tan A
• sin A
• cot A• cos A
• sin A + cos A
Answer: cot ABy definition, cosec A = 1 / sin A and sec A = 1 / cos A. So cosec A / sec A = cos A / sin A = cot A.15. For the figure given on the right, the value of cot A is • sin A / cos A
• tan C• cos C / sin C
• a / c • c / b Answer: tan CThe value of cot A is c/a. Similarly the value of tan C is c/a. Hence cot A = tan C.
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