Unit 7: Trigonometric Identities (Day 1)

Solving Trigonometric Equations Algebraically

Learning

Intentions: Solve a primary and reciprocal trig ratio for an unknown angle in

standard position

Factor expressions involving trig ratios

Recall the special triangles:

When solving, we need all values within the given domain.

Each value of sine and cosine (except 1 and -1) occurs twice within 1

cycle. Find both answers.

Examples: Solve for 20 x

i) 2

1sin x ii)

2

1cos x

iii) 2

sin5

x iv) 0tan x

v) 3

2sec x vi) 2cos3cos2 xx

45o

45o

45o = 30o

60o

30o =

60o =

We may need to factor first:

Solve for 20 x :

i) 01coscos2 2 xx

ii) 03sin4sin 2 xx

Solve for

x2

:

iii) 0coscos 2 xx

iv) 0sintansin3 xxx

v) 5cottan4 xx

vi) 1cscsin2 xx

Homework:

p. 592 #4, 6-8, 11-15