8. Introduction to Trigonometry
Trigonometry
8. Introduction of Trigonometry
SECTION = A
Q1. 
(a) 
(b) 
(c) 
(d) 
Solution: (b) .
[ We have , 
]
Q2. 
(a) tan90°
(b) 1
(c) sin45°
(d) 0
Solution: (d) 0 .
[ We have , 
]
Q3. The value of cosec31° – sec59° is :
(a) 1 (b) – 1 (c) 0 (d) 2
Solution: (c) 0 .
[ We have , 
]
Q4. 
(a) – 77 (b) 1 (c) 77 (d) 0
Solution: (a) – 77
[ We have , 
]
Q5. If 
, then the value of 
is :
(a) 
(b) 
(c) 
(d) 
Solution: (a)
[ We have , 
and 
]
Q6. If 
, then the value of 
is
(a) 45° (b) 30° (c) 60° (d) 90°
Solution: (d) 90° .
[ We have , 
]
Q7. If 
, then the value of 
is equal to :
(a) 
(b) 
(c) 
(d) 
Solution: (c)
[ Given , 
]
Q8. If 
, then value of 
is equal to –
(a) 0 (b) 
(c) 
(d) 
Solution: (a) 0 .
[ We have , 
]
Q9. The value of 
is :
(a) 1 (b) 0 (c) 
(d) 
Solution: (b) 0
[ We have ,
]
Q10. Given that 
and 
, then the value of 
is :
(a) 1 (b) 2 (c) 3 (d) 
Solution: (a) 1
[ We have , 
and 
]
Q11. Which of the following statement is true ?
(a) 
for all values of 
.
(b) The value of 
increases as increase .
(c) The value of 
increases as increase .
(d) 
is not defined for 
.
Solution: (b) The value of increases as increase .
Q12. The value of 
is equal to :
(a) 
(b) 
(c) 
(d) 
Solution: (c)
[ We have , 
]
Q13. If 
, where 
is an acute angle , then the measure of 
is :
(a) 35° (b) 37° (c) 39° (d) 21°
Solution: (c) 39°
[ We have , 
]
Q14. The value of 
is :
(a) 0 (b) 2 (c) – 2 (d) 1
Solution: (c) – 2
[ We have ,
]
Q15. If , then the value of 
is equal to –
(a) 3 (b) 5 (c) 6 (d) 8
Solution: (d) 8
[ We have , 
]
Q16. Which of the following statement is true ?
a) The value of 
is always less than 1.
(b) The value of 
is always greater than 1.
(c) 
for some angle 
.
(d) 
for some angle .
Solution: (d) for some angle .
Fill in the blanks
Q1. If 
, then the value of 
is 
.
Solution: 0
[ We have , 
]
Q2. If 
, then the value of 
is equal to 
.
Solution: 
.
[ We have , 
and 
]
Q3. If 
, then the value of the expression 
is 
.
Solution: 1
[ We have , 
]
Q4. If 
and 
, then the value of 
is 
.
Solution: 30°
[ We have , 
]
Q5. If 
, then the value of 
is 
.
Solution: 
.
[ We have , 
]
Q6. 
is equal to .
Solution: – 1
[ We have , 
]
Q7. If 
, then the value of 
is equal to 
.
Solution: 1
[ We have , 
]
Q8. If 
, then the value of 
is equal to 
.
Solution: 
.
[ Given , 
]
Q9. If 
and 
, then the value of 
is 
.
Solution: 0
[ We have , 
]
Q10. If 
, then 
equals 
Solution: 
.
[ Given ,
and 
]
Q11. The value of 
is .
Solution: 
[ We have , 
]
Q12. The value of 
is 
.
Solution: 1
[ We have , 
]
Q12. If A and 3A – 30° are acute angles such that 
, then the value of 
is
equal to .
Solution: 
.
[ We have , 
]
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