Download aim 57 key - Manhasset Public Schools

HW # 56 Answer KEY 1. II
2. I
3. √5 4. ­ 3 3 √7 5. ­√5 6. ­ 3 7. 3 8. (.31, .95)
3 5 5
9.
√2
√3
0 1 0 ­1 0
½
2
2
√3
√2
1 0 ­1 0 1
½
2
2
√3
√3
0 1 undef. 0 undef. 0 3
Mixed Review
10. 8
fill in your table!
11. (3) sinA = a/c
12. (2) ­2350
Aim 57: How do we use reference angles ? Do Now: a) Use a special right triangle to help you recall the values of sin 30, cos 30, tan 30.
P
1
b) What are the coordinates of point P in the the unit circle?
30o
P
150
210
o
o
330
o
P
P
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
point P point P
point P point P sin 30o =
sin 150o = sin 210o = sin 330o = cos 30o = cos 150o = cos 210o = cos 330o = tan 30o = tan 150o = tan 210o = tan 330o = In each of these cases, we referred back to a 30o angle. 30o is called the reference angle, and it the basis for the other angles. A reference angle is a Quadrant 1 angle. It is the angle between the x­axis and the terminal ray. 1. Find the reference angle for each of the following angles.
a) 210
b) 300
c) 125
d) ­100 e) 500
f) 250
2. Fill in the following exact values using knowledge from the unit circle and the special right triangles. 3. Express each of the following as a function of a positive acute angle.
a) sin 140o
b) cos 250o
c) tan 300o watch the
quadrants!
4. Find the exact value of each expression.
a) cos 120o
b) sin 225o
c) tan 240o
Extra Practice ­ Special Right Triangles & Reference Angles 1. Find the exact value of cos 135o.
2. Find the exact value of (sin 30o)(cos 270o)
3. Represent tan (­135o) as a function of a positive acute angle.
4. In the unit circle shown in the accompanying diagram, what are the coordinates of (x, y)?
5. Find the exact value of (sin 60o)(cos 60o)
6. In the accompanying diagram of a unit circle, the ordered pair (x, y) represents the point where the terminal side of the θ intersects the unit circle.
If θ = 120, what is the value of x in simplest form?
Sum it Up
The special right triangles allow us to give exact values of trigonometric functions of the special angles.
A reference angle is a quadrant I angle that serves as the basis for angles in other quadrants. To find the reference angle of θ, graph θ, and find the angle between the terminal ray and the x­axis.
To represent a trigonometric function as a function of a positive acute angle,
1) find the reference angle
2) think of the sign of the trig function in that quadrant
3) write the function as: (sign)trig function(reference angle). To find the exact value of a trigonometric function,
1) write the function as a function of a positive acute angle
2) use the special right triangles/unit circle to find the exact value
3) watch quadrants!