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Worksheet: Inverse Trigonometric Functions

Q1:

Find the exact value of c o s s i n 5 1 3 1 .

  • A 1 3 1 2
  • B 5 1 3
  • C 1 3 5
  • D 1 2 1 3
  • E 5 1 2

Q2:

𝐴 𝐵 𝐶 is a triangle where c o s 𝐴 = 0 . 2 3 2 7 and t a n 𝐵 = 0 . 9 3 8 1 . Find the value of 𝐶 giving the answer to the nearest minute.

  • A 1 4 6 3 8
  • B 3 3 2 2
  • C 1 0 3 2 7
  • D 6 0 1 7

Q3:

Find the exact value of c o s c o s 1 𝜋 7 in radians.

  • A 8 𝜋 7
  • B 6 𝜋 7
  • C 8 𝜋 7
  • D 𝜋 7
  • E 𝜋

Q4:

Find the exact value of c o s s i n 4 5 1 .

  • A 5 2
  • B 4 5
  • C 5 4
  • D 3 5
  • E 3 4

Q5:

Which of these two value tables shows a domain of the sine function that can be used to construct its inverse function?

Table A

𝑥 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2 2 𝜋 3 3 𝜋 4 5 𝜋 6 𝜋
s i n 𝑥 0 1 2 2 2 3 2 1 3 2 2 2 1 2 0

Table B

𝑥 𝜋 2 𝜋 3 𝜋 4 𝜋 6 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2
s i n 𝑥 1 3 2 2 2 1 2 0 1 2 2 2 3 2 1
  • A Table B
  • B Table A

Q6:

Which of the following is closest to a r c t a n ( 1 0 0 0 0 ) ?

  • A 1 8 0
  • B 0
  • C 4 5
  • D 9 0
  • E 2 7 0

Q7:

Find the exact value of c o t c o t 1 4 𝜋 3 in radians.

  • A 𝜋
  • B 𝜋 3
  • C 4 𝜋 3
  • D 𝜋 3

Q8:

Find the exact value of t a n 1 ( 1 ) , in radians in terms of 𝜋 , which is located in the 1st quadrant.

  • A 𝜋 2
  • B1
  • C0
  • D 𝜋 4
  • E 𝜋 3

Q9:

Which of these two value tables shows a domain of the cosine function that can be used to construct its inverse function?

Table A

𝑥 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2 2 𝜋 3 3 𝜋 4 5 𝜋 6 𝜋
c o s 𝑥 1 3 2 2 2 1 2 0 1 2 2 2 3 2 1

Table B

𝑥 𝜋 2 𝜋 3 𝜋 4 𝜋 6 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2
c o s 𝑥 0 1 2 2 2 3 2 1 3 2 2 2 1 2 0
  • A Table A
  • B Table B

Q10:

The given tables show some values of 𝑓 ( 𝑥 ) , 𝑔 ( 𝑥 ) , and ( 𝑥 ) . Which function corresponds to the function t a n 1 𝑥 ?

𝑥 3 1 0 1 3 1
𝑓 ( 𝑥 ) 𝜋 3 𝜋 4 0 𝜋 6 𝜋 4
𝑥 3 1 2 0 3 1
𝑔 ( 𝑥 ) 𝜋 6 𝜋 4 0 𝜋 6 𝜋 2
𝑥 1 1 2 0 1 3 3
( 𝑥 ) 𝜋 4 𝜋 6 0 𝜋 6 𝜋 3
  • A ( 𝑥 )
  • B 𝑔 ( 𝑥 )
  • C 𝑓 ( 𝑥 )

Q11:

Find the exact value of c o s c o s 1 𝜋 1 0 in radians.

  • A 9 𝜋 1 0
  • B 9 𝜋 1 0
  • C 1 0 𝜋 1 1
  • D 𝜋 1 0
  • E 𝜋

Q12:

𝐴 𝐵 𝐶 𝐷 is a parallelogram with an area of 546 cm2. The point 𝐸 is on 𝐵 𝐶 where 𝐴 𝐸 𝐵 𝐶 , the ratio between 𝐵 𝐸 and 𝐸 𝐶 is 1 3 : and 𝐴 𝐸 = 4 2 c m . Find the measure of 𝐶 giving the answer to the nearest second.

  • A 1 7 5 3 4 3 1
  • B 8 5 3 4 3 1
  • C 1 0 1 3 9 3 3
  • D 9 4 2 5 2 9

Q13:

Find the exact value of s i n s i n 1 5 𝜋 6 in radians.

  • A 5 𝜋 6
  • B 𝜋 6
  • C 𝜋
  • D 𝜋 6

Q14:

Find the exact value of t a n c o t 1 1 3 5 + 3 5 in radians.

  • A 𝜋 4
  • B 𝜋 3
  • C 𝜋 6
  • D 𝜋 2
  • E 𝜋

Q15:

Find the exact value of s i n c o s 1 1 5 1 3 + 5 1 3 in radians.

  • A 𝜋 4
  • B 𝜋 3
  • C 𝜋 6
  • D 𝜋 2
  • E 𝜋

Q16:

A man stands 5.4 m from a vertical wall. A footlight on the ground, 2.7 m from where he is standing, is switched on. If the man is 1.8 m tall and his shadow is 5.5 m tall, what angle does the light make with the horizontal? Give your answer to two decimal places.

Q17:

Find the values of 𝛼 and 𝛽 giving the answer to the nearest second.

  • A 𝛼 = 3 5 5 0 1 6 , 𝛽 = 4 6 1 4 1 8
  • B 𝛼 = 4 6 1 4 1 8 , 𝛽 = 4 3 4 5 4 2
  • C 𝛼 = 4 6 1 4 1 8 , 𝛽 = 3 5 5 0 1 6
  • D 𝛼 = 4 3 4 5 4 2 , 𝛽 = 4 6 1 4 1 8

Q18:

Find the exact value of t a n 1 ( 0 ) in radians.

Q19:

Find the exact value of s i n s i n 1 4 𝜋 3 in radians.

  • A 𝜋 3
  • B 5 𝜋 3
  • C 4 𝜋 3
  • D 𝜋 3
  • E 𝜋

Q20:

𝐴 𝐵 𝐶 is an isosceles triangle where 𝐴 𝐵 = 𝐴 𝐶 and 𝐵 𝐶 = 2 4 c m . The point 𝐷 lies on 𝐵 𝐶 where 𝐴 𝐷 𝐵 𝐶 and 𝐴 𝐷 = 1 6 c m . Find the length of 𝐴 𝐶 giving the answer to the nearest centimeter and the value of 𝐶 giving the answer to the nearest second.

  • A 𝐴 𝐶 = 1 2 c m , 𝑚 𝐶 = 5 3 7 4 8
  • B 𝐴 𝐶 = 2 0 c m , 𝑚 𝐶 = 3 6 5 2 1 2
  • C 𝐴 𝐶 = 1 6 c m , 𝑚 𝐶 = 3 6 5 2 1 2
  • D 𝐴 𝐶 = 2 0 c m , 𝑚 𝐶 = 5 3 7 4 8