Trigonometric Ratio

CONTENT

• Basic trigonometric Ratio
• Ratio of General Angle
• Trigonometric Identities

Reciprocals of Basic Ratios

We define the reciprocals of the three basic ratios as:

Secant of angle Ө =   PQ/PR    = r/q   = 1 / cosine of angle Ө.

Cosecant of angle Ө = PQ / QR = r / q = 1 / sine of angle Ө

Cotangent of angle Ө = PR / QR   = q / p =   1 / tangent of angle Ө

The secant of angle Ө, the cosecant of angle Ө and the cotangent of angle Ө are abbreviated secӨ, cosecӨ and cotӨ respectively.

            SecӨ   = r / q   = 1 / cosӨ

            CosecӨ   = r / p =   1 / sinӨ

            CotӨ =   q / p =   1 / tanӨ   =   cosӨ / sinӨ

Ratios of General Angles

GRAPH OF SINE AND COSINE FOR ANGLES

WEEKEND ASSIGNMENT 

Given that sin Ө = 4/5 and Ө is acute

1. find cos Ө (a) 5/3 (b) 3/5 (c) 4/3 (d) 4/5
2. find tan Ө (a) 4/5 (b) 3/5 (c) 5/4 (d) ¾
3. find cosec Ө (a) 4/5 (b) 3/5 (c) 5/4 (d) ¾
4. find sec Ө (a) 5/3 (b) 5/4 (c) ¾ (d) 5/2
5. find cot Ө (a) 3/5 (b) 4/5 (c) 5/4 (d) 5/3