Cotangent, identities and solving right triangles
Learn the cotangent and the main trigonometric identity, solve right triangles from a hypotenuse and an angle or from two legs, and solve practical problems. Section: Grade 8, right triangles; any triangle is in the Grade 9 studio.
- Ukraine: grade 8
- Russia: grade 8
Guide
In the Ukrainian programme this is Grade 8 geometry, §3: item 17 "Trigonometric functions of an acute angle of a right triangle" and item 18 "Solving right triangles".
In right-angled triangle ABC with the right angle at C, for the acute angle A: sin A = BCAB, cos A = ACAB, tg A = BCAC, ctg A = ACBC. BC is opposite A, AC is adjacent, AB is the hypotenuse. The names: sine, cosine, tangent, cotangent.
The main identity: sin2α + cos2α = 1. Also tgα = sinα/cosα and tgα·ctgα = 1.
To solve a right triangle means to find all its sides and angles from two known parts (one must be a side). This solves practical problems about height, slope and distance.