what is trigonometric ratios
Answers
Answer:
the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.
Answer:
Trigonometric ratios are the ratios used in solving problems related to trigonometry. There are six of them and hold good in relating angles of a right triangle with their respective sides (refer to attachment 1).
• sin θ = opposite side/hypotenuse (AB/AC)
• cos θ = adjacent side/hypotenuse (BC/AC)
• tan θ = opposite side/adjacent side (AB/BC)
• cosec θ = hypotenuse/opposite side (AC/AB)
• sec θ = hypotenuse/adjacent side (AC/BC)
• cot θ = adjacent side/opposite side (BC/AB)
where θ is the angle apart from the right angle of the right triangle, and the opposite side and adjacent side are with respect to θ.
Some special relations (in terms of sin θ and cos θ):
• tan θ = sin θ/cos θ
• cot θ = cos θ/sin θ
• cosec θ = 1/sin θ
• sec θ = 1/cos θ
Each of the trigonometric ratios have specific values for specific angles (refer to attachment 2).
Trigonometric ratios of complementary angles:
• sin (90° - θ) = cos θ
• cos (90° - θ) = sin θ
• tan (90° - θ) = cot θ
• cot (90° - θ) = tan θ
• cosec (90° - θ) = sec θ
• sec (90° - θ) = cosec θ
Trigonometric identities:
• sin² θ + cos² θ = 1
• cosec² θ - cot² θ = 1
• sec² θ - tan² θ = 1
