INVERSE COMPLEMENTARY ANGLES

Complementary angles and supplementary angles are defined by adding two angles together. When the total of two angles equals 180 degrees, they are referred to be supplementary angles, and they produce a linear angle when combined. When the sum of two angles equals 90 degrees, they are considered to be complementary angles, and they produce a right angle when they are combined.

COMPLEMENTARY ANGLES

Complementary angles are formed when the total of two angles equals 90 degrees. In other words, complementary angles are formed when two angles are added together to make a right angle. The two angles are said to complement each other in this case.

Assume one of the angles is x, and the other is 90 degrees – x. As a result, complementary angles are used for trigonometry ratios in which one ratio complements another by 90 degrees, such as

• sin sin (90°- A) =cos cos A and cos cos (90°- A )=sin sin A
• tan tan (90°- A )=cot cot  A and cot cot (90°- A) =tan tan A
• sec sec (90°- A) = cosec A and cosec (90°- A)=sec sec  A

PROPERTIES OF COMPLEMENTARY ANGLES

Complementary angles have the following properties:

• If two angles SUM are up to 90 degrees, they are considered to be complimentary.
• They can be next to each other or not.
• Even if the sum of three angles is 90 degrees, they cannot be complementary.
• When two angles are complementary, one of them is referred to as the “complement” or “complement angle” of another.
• A right-angled triangle’s two acute angles are complementary.

SUPPLEMENTARY ANGLES

Supplementary angles are formed when the total of two angles equals 180 degrees. In other words, supplementary angles are formed when two angles are added together to make a straight angle.

The two angles constitute a linear angle, with one angle equal to x and the other equal to 180 – x. The fact that the angles are linear demonstrates that their qualities do not change. Consider the following trigonometric ratios:

• Sin (180 – A) = Sin A
• Cos (180 – A) = – Cos A (quadrant is changed)
• Tan (180 – A) = – Tan A

If the total of two angles equals 90 degrees, they are complimentary in geometry. Similarly, the mathematical equations for complementary angles may be learned here.

• Sin (90 – θ) = Cos θ
• Cos (90 – θ) = Sin θ
• Tan (90 – θ) = Cot θ
• Cot ( 90 – θ) = Tan θ
• Sec (90 – θ) = Csc θ
• Csc 90 – θ= Sec θ

Supplementary Angles’ Trigonometric Identities

If the total of two angles equals 90 degrees, they are supplementary. Similarly, the trigonometric identities of supplementary angles may be learned here sin (180°- θ) = sinθ

• cos (180°- θ) = -cos θ
• cosec (180°- θ) = cosec θ
• sec (180°- θ)= -sec θ
• tan (180°- θ) = -tan θ
• cot (180°- θ) = -cot θ

CONCLUSION

We learned the definition of complementary angles, their applications, and the trigonometric ratios of various angles in the preceding subject. We’ve also learned about the link between trigonometric ratios and their identities.

We also learned how to calculate trigonometric ratios for complementary angles & solved various issues using these ratios.