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Transcript
```Math 170
Trigonometry Lecture Notes
Chapter 6
6.1 & 6.2 Trigonometric Equations
6.1 Solve using factoring, quadratic formula, or horizontal translations
6.2 Solve using identities, clearing denominators, or squaring both sides
[CA – Review problems 6.1 # 77, 79, 81]
Basic Concepts for Solving Trigonometric Equations:
Goal: To get ONE trig function equal to a number.
Method Depends on the Type of Equation:
♦ Two Functions in One Equation:
o Try Factoring
o Use Pythagorean Identities to Change to One Function (may need to square in
order to do this)
♦ Fractions: Clear the denominators by multiplying by LCD
♦ Since Trigonometric Functions are periodic, they repeat.
o For sin, cos, csc & sec add ________________
o For tan & cot add ______________
B) Solve. Find the solutions in the interval [0, 2π)
1) (sin x – 1) (sin x + 2) = 0
3)
2) 2 cos2x – cos x = 1
2 tan θ
=1
3 − tan 2 θ
CA 6.1 11, 19, 33
6.2 #7, 37, 43
1
Math 170
Trigonometry Lecture Notes
Chapter 6
Applications:
If a projectile is fired into the air with an intial velocity v at an angle of elevation θ, then the
height h of the projectile at time t is given by
(see picture pg 327, 6.1 problem set)
h = -16t2 + v∙t sinθ
6.1 #72 Give the equation for h if v is 600 feet per second and θ is 45o (Leave answer in exact
form.)
6.1 #74 Use the equation you found in #72 to find the height of the object after 3 seconds
(round solution to the nearest tenth).
CA 6.1 #76
2
Math 170
Trigonometry Lecture Notes
Chapter 6
6.3 Trigonometric Equations of Multiple Angles
Solve the equations: (a) Find all Solutions and (b) Find solutions in the Interval [0, 2π)
1) 3 tan 3 x = 3
2) − 2 cos 2 x =
3
3) cos 2θ – cos θ = 0
CA 6.3 #15, 25, 39
3
```