Nayland College, Nelson, co-educational high school ...
Angles can be measured 3 different ways:
Degrees (1 revolution = 360° and ¼ turn = 90°)
Grads (1 revolution = 400 grad and 90° = 100 grad) - engineering
Radians (1 revolution = 2π and 180° = π radians)
Definition: 1 radian angle makes an arc length of 1 radius
π radians = 180°
so 1 radian = 180/π degrees
and π/180 radians = 1°
Convert to radians
1) 270° = _____ 2) 25° = _____
Convert to degrees
3) π/4 = _____ 4) 3π/2 = _____
π radians = 180°
y = Sin(x) y = Cos(x)
Features Features y = Tan(x)
Features
To avoid decimal values, radians are given as fraction of π
Quadrant 1 All positive Calculator answer
Quadrant 2 Sin positive Subtract from π
Quadrant 3 Tan positive Add to π
Quadrant 4 Cos positive Subtract from 2π
1) Solve Cos(x) = 0.4 0 < x < 2π
Positive, so in ‘ALL’ and ‘Q4’
Solutions ‘ALL’ Cos-1(0.4) = 1.16
‘Q4’ 2π – 1.16 = 5.12 radians
2) Solve Sin(x) = -0.2 0 < x < 2π
Negative, so in ‘Q3’ and ‘Q4’
Sin-1(0.2) = 1.772
Solutions are ‘Q3’ π + 1.772 = 4.914
or ‘Q4’ 2π – 1.772 = 4.511
Solving Equations in radians:
Use the same process, Using our calculator in radians mode,
and using π & 2π instead of 180° & 360°
Solve Sin(x) = 0.7 Where does the y = Sin(x) graph have y = 0.7?
Find all solutions between x = 0 and 2π
[pic]
Solve Sin(x) = -0.25 0 < x < 2π
-----------------------
C
T
A
S
S
C
T
A
0 2π
π
π
2π
Calculator gives 1 solution
How do we get the other?
π
2π
Trig Equations: Radians
Theta
Ex 34.03
0 2π
π
Hw p154
Sin
Cos
Tan
All
Q4
Q3
Q1
Q2
0 2π
π
Sin
Cos
Tan
All
Q4
Q3
Q1
Q2
0 2π
π
Trig Graphs with Radians
Trig Equations: Radians
Theta
Ex 33.01
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