ib maths unit circle exact values
TRANSCRIPT
• Define tangent of an angle in the unit circle and in terms of sine and cosine.
• Find the exact values of sine, cosine and tangent of the most used angles.
By the end of the lesson you will be able to:
Trigonometry: Exact values of sine and cosine
Tangent of an angle in the unit circle.
x
y or
Tangent of an angle in the unit circle.
x
yy' or
Tangent of an angle in the different quadrants.
y'
Conclusions:tan 90o and tan 270o don't exist.tan θ is positive in quadrants I and III and negative in quadrants II and IV
drag the orange line around the circle.
y' tan (πα) =
tan (α + π) =
tan (2πα) =
α
Express in terms of tan α:
Exact values Sine and cosine of 45o
Then tan 45o =
Exact values Sine and cosine of 60o and 30o
Complete with the exact values:
tan α
0
tan α
0
0
0
1
1
1
Find the exact value of : a) sin 120o
Find the exact value of : b) cos 315o
Find the exact value of : c) sin
Find α , 0 ≤α≤360o, such that : sin α =
Find α , 0 ≤α≤360o, such that : cos α =
Find α , 0 ≤α≤360o, such that :
cos α =sin α = and