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In this lesson, we will learn how to calculate exact values of trigonometric inverses and how to recognize the inverse of trigonometric functions from tables.

Q1:

The given tables show some values of π ( π₯ ) , π ( π₯ ) , and β ( π₯ ) . Which function corresponds to the function s i n ο± ο§ π₯ ?

Q2:

The given tables show some values of π ( π₯ ) , π ( π₯ ) , and β ( π₯ ) . Which function corresponds to the function t a n ο± ο§ π₯ ?

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Table A

Table B

Q7:

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

Q8:

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

Q9:

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

Q10:

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

Q11:

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

Q12:

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

Q13:

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

Q14:

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

Q15:

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

Q16:

Find the values of πΌ and π½ giving the answer to the nearest second.

Q17:

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

Q18:

π΄ π΅ πΆ is a triangle where c o s π΄ = 0 . 2 3 2 7 and t a n π΅ = 0 . 9 3 8 1 . Find the value of β πΆ giving the answer to the nearest minute.

Q19:

π΄ π΅ πΆ π· is a parallelogram with an area of 546 cm^{2}. The point πΈ is on π΅ πΆ where π΄ πΈ β π΅ πΆ , the ratio between π΅ πΈ and πΈ πΆ is 1 3 : and π΄ πΈ = 4 2 c m . Find the measure of β πΆ giving the answer to the nearest second.

Q20:

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.

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