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In this section we will discuss about trigonometry for specific angles.We have already learned that trigonometry is the study of relationships between the sides and angles of a triangle. The ratios of the sides in a right triangle with respect to some acute angles are called trigonometry for specific-angles. The angles 0

When two angles add up to 90

| sin 0^{0} = 0cos 0 ^{0} = 1 tan 0 ^{0} = 0 |
csc 0^{0} = Not defined sec 0 ^{0} = 1 cot 0 ^{0} = undefined |

| sin 30^{0} = 1 / 2cos 30 ^{0} = √3 / 2 tan 30 ^{0} = 1 / √3 |
csc 30^{0} = 2 sec 30 ^{0} = 2 / √3 cot 30 ^{0} = √3 |

| sin 45^{0} = 1 / √2cos 45 ^{0} = 1 / √2 tan 45 ^{0} = 1 |
csc 45^{0} = √2 sec 45 ^{0} = √2 cot 45 ^{0} = 1 |

| sin 60^{0} = √3 / 2cos 60 ^{0} = 1 / 2 tan 60 ^{0} = √3 |
csc 60^{0} = 2 / √3sec 60 ^{0} = 2 cot 60 ^{0} = 1 / √3 |

1) Evaluate : ( sin

( sin

= 1 / tan

= 1/ (√3)

= 1 / 3

_______________________________________________________________

2) 2 sin

2 sin

= 2 ( 1/ 2)

= 2 x 1 / 4 x √ 3 – 3 x ¼ x 4 / 3

= √3 / 2 – 1

= ( √3 – 2 ) / 2

_______________________________________________________________

3) Solve tan 5A = 1 for 0

tan 5A =1

5A = 45

A = 45/5

A = 9

_______________________________________________________________

4) Find the acute angles A and B, if sin(A + 2B) = √3 / 2 and

cos (A + 4B ) = 0, A>B.

sin(A + 2B) = √3 / 2

sin(A + 2B) = sin 60

A + 2B = 60 ------> (1)

cos (A + 4B ) = 0

cos (A + 4B ) = cos 90

A + 4B = 90 -----------> (2)

Subtract equation (1) from (2) we get

2B = 30

B = 15

Equation (1)

A + 2(15) = 60

A + 30 = 60

A = 60 – 30

A = 30

• SOHCAHTOA -Introduction to Trigonometry

• Trigonometric ratios and their Relation

• Trigonometry for specific angles

• Complementary angles in Trigonometry

• Trigonometric Equations

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