Revision Material Ch 33. Trigonometric Ratios - 1

I.
Function-------------Domain--------------Range

Sin θ------------------R----------------[-1,1]

cos θ------------------R-----------------[-1,1]

tan θ------------R-{(2n+1)π/2, nЄI}------R=(-∞. ∞)




II.Basic relations

sin θ*cosec θ = 1

cos θ*sec θ = 1

tan θ*cot θ = 1

sin² θ + cos² θ = 1

sec²θ - tan²θ =1; 1 + tan² θ = sec² θ

cosec²θ - cot²θ = 1; 1+cot2θ = cosec²θ


III. Allied or Related angles

1. sin (-θ) = -sin θ
2. cos(-θ) = cos θ



IV.Compound angles

1. sin (A+B) = sin A cos B + cosA sin B

2. sin 2A = 2 sin A cos A

3. sin (A-B) = sin A cos B - cos A sin B

4. cos (A+B) = cos A cos B -sin A sin B

5 cos 2A = cos²A - sin²A

6. cos (A-B) = cos A cos B + sin A sin B