Trigonometry for Specific AnglesIn 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 0 , 30 0 , 45 0 , 60 0 and 90 0 are useful angles in trigonometry, and their numerical values are easy to remember.These are trigonometry for specific angles.
When two angles add up to 90 0 , then any one angle is the complement of the other. Trigonometric ratios of complementary angles help in simplifying problems.
Trigonometric Ratios of 00 Trigonometric Ratios of 300 Trigonometric Ratios of 450
Trigonometric Ratios of 600
Some Solved Examples on trigonometry for specific angles:
1) Evaluate : ( sin 2 45 0 + cos 2 45 0 ) / tan 2 60 0
Solution :
( sin 2 45 0 + cos 2 45 0 ) / tan 2 60 0
= 1 / tan 2 60 0 [ since sin 2 θ + cos 2 θ = 1 ]
= 1/ (√3) 2
= 1 / 3
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2) 2 sin 2 30 0 tan 60 0 - 3 cos 2 60 0 sec 20
Solution :
2 sin 2 30 0 - 3 cos 2 60 0 sec 20
= 2 ( 1/ 2) 2 x √3 – 3 ( ½) 2 x (2 / √3) 2
= 2 x 1 / 4 x √ 3 – 3 x ¼ x 4 / 3
= √3 / 2 – 1
= ( √3 – 2 ) / 2
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3) Solve tan 5A = 1 for 0 0 < A < 90 0
Solution :
tan 5A =1
5A = 45
A = 45/5
A = 9 0
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4) Find the acute angles A and B, if sin(A + 2B) = √3 / 2 and
cos (A + 4B ) = 0, A>B.
Solution :
sin(A + 2B) = √3 / 2
sin(A + 2B) = sin 60 0
A + 2B = 60 ------> (1)
cos (A + 4B ) = 0
cos (A + 4B ) = cos 90 0
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
Trigonometry
• SOHCAHTOA -Introduction to Trigonometry
• Trigonometric ratios and their Relation
• Trigonometry for specific angles
• Complementary angles in Trigonometry
• Trigonometric Equations