Define sine, cosine, tangent, and their reciprocals relative to an acute angle in a right triangle.
Preview · progress not saved — Chapter 1 is free
Right-angled triangle showing opposite and adjacent sides for Angle A.
A clean scientific diagram of a right-angled triangle ABC. The 90-degree angle is marked at vertex B. Vertex A is an acu…
Introduce terms: Hypotenuse, Side Opposite, Side Adjacent.
When working with right triangles, correctly identifying the sides is the crucial first step to learning trigonometry. The hypotenuse is always the longest side, and it is positioned directly opposite the angle. Its position never changes, regardless of which acute angle you focus on.
Formulas for sine, cosine, and tangent of Angle A.
Important: is a single mathematical symbol meaning 'the sine of angle A'. It is not the word 'sin' multiplied by 'A'. The same applies to all trigonometric ratios.
Formulas for cosecant, secant, and cotangent of Angle A.
Explain that trig ratios depend only on the angle, not the size of the triangle.
Imagine taking a point on the extended hypotenuse of right triangle and drawing a new line perpendicular to the extended base . This creates a new, larger right triangle, .
Because both triangles share angle and both have a angle, they are similar by the AA (Angle-Angle) similarity criterion ().
Match sin, cos, tan, etc., to their side-based definitions.
Terms
Definitions
Determine if statements about abbreviations and definitions are correct.
Is the following statement true or false? 'cos A is the abbreviation used for the cosecant of angle A.'