2.1 Trigonometric Functions of Acute Angles

Introduce traditional triangle definitions

Hence …. SOH / CAH / TOA

Example

Find the sine, cosine, and tangent for angles D and E

Co function Identities

For any acute angle A.

Write each function in terms of its co function

a) sin 9^o

b) cot 76 ^o

c) csc 45 ^o

Find one solution for each equation. Assume all angles are acute.

a) cot (θ - 8^o) = tan(4θ + 13^o)

b) sec(5θ + 14^o) = csc(2θ – 8^o).

As θ increases from 0 ^o to 90 ^o, what happens to sin θ?

sin A increases as A increases from 0 to 90^o

cos A decreases as A increases from 0 to 90^o

tan A increases as A increases from 0 to 90^o

The co functions do the opposite.

True or False

a) tan 25^o < tan 23^o

b) csc 44^o < csc 40^o

c) sin 44^o > sin 40^o

Trigonometric Values of Special Angles

Using triangles, consider an equilateral triangle, divided into two congruent triangles by the altitude.

Each of these triangles is a 30-60-90 triangle which can be used to find the values of the trig functions for 30^o or 60^o.

sin 30 = cos 30 = tan 30 =

csc 30 = sec 30 = cot 30 =

sin 60 = cos 60 = tan 60 =

csc 60 = sec 60 = cot 60 =

Consider an isosceles right triangle. This can be used to find the trigonometric functions for 45^o

sin 45 = cos 45 = tan 45 =

csc 45 = sec 45 = cot 45 =

Table of Trigonometric Values of 30 ^o, 60 ^o, and 45 ^o

θ	sinθ	cosθ	tanθ	cotθ	secθ	cscθ
30^o						2
45^o			1	1
60^o					2