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: If the shadow of a tower is 30 metres, when the sun's altitude is 30^{o}, what is the length of the shadow when the sun's altitude is 60^{o}? Answer:

Q 2: Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length 10 cm 3/15 2/15 4/15

Q 3: 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. 100 m 203^{1/2} m 20 m

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

Q 5: The angle of elevation of the top of a tower which is yet incomplete at a point 120 metres from its base is 45^{o}. How much higher should it be raised so that the elevation at the same point may become 60^{o}? 87.84 metres 36.85 metres 100 metres

Q 6: In triangle ABC, if b = 6, c = 4, cos A = 1/12, find a 4.3^{1/2} 3^{1/2} 4

Q 7: In triangle ABC, a = 8.4 cm, b = 7.6 cm and c = 9.2 cm. Calculate the area of triangle ABC. 30 sq cm 45 sq cm 50 sq. cm

Q 8: 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

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Question 10: This question is available to subscribers only!