Trigonometric Functions - Unit Circle Approach Worksheet Page 5
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1
2
3
4
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7
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9
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sin(θ θ θ θ )
cos(θ θ θ θ )
tan(θ θ θ θ )
csc(θ θ θ θ )
sec(θ θ θ θ )
cot(θ θ θ θ )
θ θ θ θ
θ θ θ θ
0
0˚
0
1
0
1
undefined
undefined
π
90˚
1
0
1
0
undefined
undefined
2
180˚
0
– 1
0
– 1
π
undefined
undefined
3 π
270˚
– 1
0
– 1
0
undefined
undefined
2
Definition:
Two angles are coterminal if they have the same initial and terminal sides.
Properties of Coterminal Angles
1)
Two coterminal angles with differ by integer multiplies of 2 π (360˚)
2)
The Trig. value of two coterminal angles are equal.
Find the following:
Ex. 4a
sin(– 450˚)
Ex. 4b
tan(9 π )
Solution:
Solution:
A coterminal angle to – 450˚ is
A coterminal angle to 9 π
– 450˚ + 2 • 360˚ = 270˚.
is 9 π – 4 • 2 π = π
So, sin(– 450˚) = sin(270˚) = – 1
So, tan(9 π ) = tan( π ) = 0
Objectives 3 & 4: Find the Exact Values of the Trigonometric Functions of
for Special Angles
The first special right triangle we want to examine is a 45˚-45˚-90˚ right
triangle. Since two of the angles are the same, that means two of the sides
are equal, so we have an isosceles triangle. Also, the two equal sides of
the isosceles triangle are the legs of the right triangle since the hypotenuse
is always opposite of the right angle. The hypotenuse of the triangle will be
equal to 1 since we are on the unit circle. If we let a be the length of one of
the equal sides, then we can the Pythagorean Theorem to find a.
2
2
2
2
1
= a
+ a
= 2a
45˚
1
1
2
= a
(take the square root)
a
2
1
2
a =
=
(ignore – answer)
2
45˚
2
a
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