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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