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Math : Trigonometry
Practice Exercise for Trigonometry Module 1 : Trigonometric Functions

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1. For the figure given on the left, the value of sin C is
• a / b
• b / a
• a / c
• c / a
• c / b
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
• (a + c)/b
• (b + c)/a
• (a + b)/c
• (a - b)/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
• b / a
• c / a
• c / b
• b / c
• a / b
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
• cot A = c / a
• cos A = b / c
• tan A = a / b
• sec A = b / a
Answer: cot A = c / a
By 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
• 2a/b
• a/b + c/b
• 2b/a
• b/c + c/a
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 A
The 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
• 1 / sin A
• sec A
Answer: sec A
tan 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 cosec A
• 1 + cos A
• 2 cos A
Answer: 2 cos A
We 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
• cos A
• 1
• 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 = 1
Answer: cos A sec A = 1
By definition, sec A = 1 / cos A. So cos A sec A = 1 is true.


12. From the figure, the value of sin2 A + cos2 A is
• a/b + c/b
• 1
• b/a + c/b
• (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 sin2 A + cos2 A = (a2 + c2) / b2. By Pythagoras Theorem, a2 + c2 = b2 for a right-angled triangle. Hence sin2 A + cos2 A = 1, which is a famous identity.


13. From the figure, the value of cot C + cosec C is
• (a + c)/b
• (c + b)/a
• a/c + c/b
• (a + b)/c
• 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 A
By 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
• cos C / sin C
• a / c
• c / b
• tan C
Answer: tan C
The value of cot A is c/a. Similarly the value of tan C is c/a. Hence cot A = tan C.



  Try the Quiz :     Practice Exercise for Trigonometry Module 1 : Trigonometric Functions


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