Question

(180-theta)
what answer​

Answer 1

Answer:

What are the relations among all the trigonometrical ratios of (180° - θ)?

In trigonometrical ratios of angles (180° - θ) we will find the relation between all six trigonometrical ratios.

We know that,

sin (90° + θ) = cos θ

cos (90° + θ) = - sin θ

tan (90° + θ) = - cot θ

csc (90° + θ) = sec θ

sec ( 90° + θ) = - csc θ

cot ( 90° + θ) = - tan θ

and

sin (90° - θ) = cos θ

cos (90° - θ) = sin θ

tan (90° - θ) = cot θ

csc (90° - θ) = sec θ

sec (90° - θ) = csc θ

cot (90° - θ) = tan θ

................

Therefore, sin (180° - θ) = sin θ, [since cos (90° - θ) = sin θ]

cos (180° - θ) = cos (90° + 90° - θ)

= cos [90° + (90° - θ)]

= - sin (90° - θ), [since cos (90° + θ) = -sin θ]

Therefore, cos (180° - θ) = - cos θ, [since sin (90° - θ) = cos θ]

tan (180° - θ) = cos (90° + 90° - θ)

= tan [90° + (90° - θ)]

= - cot (90° - θ), [since tan (90° + θ) = -cot θ]

Therefore, tan (180° - θ) = - tan θ, [since cot (90° - θ) = tan θ]