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MATH 1113 PreCalculus Section 6.2 notes The equation for the _______ circle, meaning _______ centered at the origin, is __________________.
- If I gave you , fill in the missing values.
- On the calculator, press the mode button and set it on DEGREE if not there already. Notice the other choice it RADIAN.
- What does sin 20° = ___________? Cos 20° = ___________?
- On the calculator, find sin θ and cos θ for a few of the above angles. SWITCH BACK AND FORTH BETWEEN RADIANS AND DEGREES UNDER THE MODE BUTTION TO ENTER SOME ANGLES AS RADIANS AND SOME AS DEGREES. Write out what they equal near the boxes or circles above.
P(____, .342) Degrees 20° Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ = 360° Radians _____ = 2π
P(____, ____) Degrees _____ Radians _____
P^22 ,____ Degrees _____ Radians π 4
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
P(½, ____) Degrees 60° Radians _____
P(____, ½ ) Degrees 30° Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
P(____, ____) Degrees _____ Radians _____
Unit circle approach Right angle approach
Above, we discovered the following definitions:
sin θ = y -coordinate of a point P( x,y ) on the unit circle (radius = 1) cos θ = x -coordinate of a point P( x,y ) on the unit circle (radius = 1)
Likewise, the following definitions are true for any circle of radius r
r
y
sin θ = (in this case
r
y is equal to the y -coordinate of a point P( x,y ) on the unit circle)
r
x
cosθ = (in this case
r
x is equal to the x -coordinate of a point P( x,y ) on the unit circle)
1 45° (^2)
2
2
2
Notice that (^1) 2
2 2
2
2 2 ^ =
+
P ( x , y ) =
2 ,^2 2
(^2) at a 45°angle
therefore sin 45° = ______
and cos 45° = ______
2
3
2
1 1 Notice that^1 2
1 2
3 2 2 =
+
P ( x , y ) =
2 ,^1 2
(^3) at a 30°angle
therefore sin 30° = ______
and cos 30° = ______
30°
2
3
2
1
(^1) Notice that 1 2
1 2
3 2 2 =
+
P ( x , y ) =
2 ,^3 2
(^1) at a 60°angle
therefore sin 60° = ______
and cos 60° = ______
60°
Quadrantal angles
θ (Radians) θ (Degrees) sin θ cos θ tan θ csc θ sec θ cot θ
0
π
Angles of 30°, 45°, 60°
θ (Radians) θ (Degrees) sin θ cos θ tan θ csc θ sec θ cot θ
Find the exact values of the following after drawing the angle on the unit circle:
a) cos 210° b) 4
sin
c) 6
csc
d) tan 4
Use the calculator to find the following. Draw the angle before calculating.
a) sin 52° b) tan 5
c) sec 5
Determine whether the following is positive or negative, without using a calculator. Then check your answer. This is to help you understand the definition of a radian from section 6.1. a) cos 3 b) cos -1 c) sin 6
Give the area of the following triangle (from the unit circle) as a function of the angle θ.
A bh 2
= = _______________
Find the area of the above triangle if θ = 30° by using the above formula and the formula
A bh 2
Give the area of the following triangle (NOT from the unit circle) as a function of the angle θ.
A bh 2
= = _______________
Find the area of the above triangle if θ = 30° by using the above formula and the formula
A bh 2
θ
θ
