It follows from the above definition that θ and ( 90 - θ ) are complementary angles in trigonometry for an acute angle θ

In ΔABC, ∠B = 90

∴ ∠A + ∠C = 90

∠C =90

For the sake of easiness in this derivation, we will write ∠C and ∠A as C and A respectively

Thus

C = 90

sin A = BC / AC cosec A = AC / BC

cos A = AB / AC sec A = AC / AB

tan A = BC / AB cot A = AB / BC

sin C = sin (90

cos C = cos (90

tan C = tan (90

sin (90^{0} - A) = cos A tan(90^{0} - A) = cot A sec(90^{0} - A) = cosec Acos (90 ^{0} - A) = sin A cot(90^{0} - A) = tan A cosec (90^{0} - A) = sec A |

This means, for example

sin 70

The cofunction of the sine is the cosine. And 20° is the complement of 70°.

1) Evaluate : cos 37

cos 37

________________________________________________________________

2) Show that : ( cos 70

( cos 70

= [ cos ( 90

= sin 20

= 1 + 1 – 2

= 0

∴ ( cos 70

• SOHCAHTOA -Introduction to Trigonometry

• Trigonometric ratios and their Relation

• Trigonometry for specific angles

• Complementary angles in Trigonometry

• Trigonometric Equations

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