High School Mathematics - 2 10.18 Trignometry Review

Function

0^{o}

30°

45°

60°

90°

sin

Ö0/2

Ö1/2

Ö2/2

Ö3/2

Ö4/2

cos

Ö4/2

Ö3/2

Ö2/2

Ö1/2

0

tan

0

Ö3/3

1

Ö3

undefined

sec

1

2Ö3/3

Ö2

2

undefined

csc

undefined

2

Ö2

2Ö3/3

1

cot

undefined

Ö3

1

Ö3/3

0

sin

cos

tan

0

0

1

0

90

1

0

infinity

180

0

-1

0

270

-1

0

infinity

Functions of angles in all quadrants in terms of those in quadrant 1

-A

90^{0} ± A P/2 ± A

180^{0} ± A P ± A

270^{0} ± A 3P/2 ± A

360^{0} ± A 2P ± A

sin

-sinA

cos A

±sin A

-cosA

±sin A

cos

cos A

±sin A

-cos A

±sin A

cos A

tan

-tan A

±cot A

± tan A

±cot A

±tan A

csc

-csc A

sec A

± csc A

-sec A

±csc A

sec

sec A

± csc A

-sec A

±csc A

sec A

cot

-cot A

± tan A

± cot A

±tan A

± cot A

Q 1: Find the degree measure of the angle subtended at the centre of a circle of diamter 200 cm by an arc of length 22cm. 45^{o} 33^{o} 12^{o}36^{l}

Q 2: The sines of the angles of a triangle are in the ratio of 4:5:6, find the ratio of the cosines of the angles. 4:5:2 2:3:4 12:9:2

Q 3: cos 75^{o} Answer:

Q 4: If tan C = 11, find sin C. cos C. Answer:

Q 5: If in two circlesarcs of the same length subtend angles 60^{o} and 75^{o} at the centre, find the ratio of their radii. 2:3 1:2 5:4

Q 6: The horizontal distance between two towers is 60 metres and the angular depression of the top of the first as seen from the top of the second, which is 150 metres is 30^{o}. Find the height of the first. 100 metres 120 metres 115.36 metres

Q 7: Show that cot x.cot 2x - cot 2x cot 3x - cot 3x cot x = 1 Answer:

Q 8: The angle of elevation of the top of a tower from a point 60m from its foot is 30^{o}. Find the height of the tower. 20 m 203^{1/2} m 100 m

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Question 10: This question is available to subscribers only!