This document contains notes on trigonometry ratios for angles in standard position. It discusses positive and negative angles, co-terminal angles which have the same arm position, and finding trig ratios given a point on the unit circle. Examples are provided to find trig ratios given angle measures or point locations, as well as using one ratio to find others. Reciprocal trig functions are also defined. Homework problems are assigned at the end.

1. 6.1 trignotes.notebook April 01, 2013
Chapter 6: Trigonometry
6.1 Trig Ratios for angles in standard position.
In Grade 11 you learned the exact values of sine,
cosine, and tangent for 30°, 45°, 60°, and 90° angles
from [0° , 360°]. This year we will expand on
that concept and learn a new way to identify angles.
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Positive and Negative Angles
If an angle rotates in a COUNTER­clockwise direction from
the positive x axis, it form a POSITVE ANGLE in STANDARD position.
Notice the angles can be greater than 360°.
When the angle rotates clockwise, then we have a negative angle.
Again, it can be more than ­360°.
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Angles that end up in the same standard position are called
CO­TERMINAL ANGLES. This means the arm is in the
same position. There are an INFINITE number of positive and
negative co­terminal angles for any angle.
Ex) Give 2 positve and 2 negative angles that are co­terminal to
40°.
Ex) Write a negative angle that is co­terminal to 100°.
Ex) Write a positive angle that is co­terminal to ­19°.
Ex) What reference angle in Quadrant 1 is in the same position
as 500°.
Ex) Write a statement for all angles co­terminal to 30°.
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Ex) P(3,4) is a terminal point of an angle in standard position.
Find the values of sine, cosine, and tangent.
Ex) P(1,­3) is a terminal point of an angle in standard position.
Find the values of sine, cosine, and tangent.
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7. 6.1 trignotes.notebook April 01, 2013
Each of these three trig ratios, has a reciprocal.
The reciprocal of sine is cosecant.
The reciprocal of cosine is secant.
The reciprocal of tangent is cotangent.
Therefore:
Ex) If the value of sin = 0.5, what is the value of csc ?
If the value of cot = ­3, what is the value of tan ?
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8. 6.1 trignotes.notebook April 01, 2013
QUESTION TYPES:
1) Given a point location, determine the trig ratios
.
Ex)
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2) Given ONE ratio, find other ratios, and angles
Ex) If and is in Quadrant 2, find the values of the
other 5 trig functions and the possible values of from [0°,360°]
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3) Given an angle, determine the TRIG RATIOS
Note: a) find the co­terminal angle for 510°. Do you remember the EXACT
values of SINE, COSINE, and TANGENT for this angle?
b) use your calculator to enter the NEGATIVE angles and find the ratios
using it INVERSE feature.
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12. 6.1 trignotes.notebook April 01, 2013
If we make the radius of the circle become "1" (known as
the UNIT CIRCLE), then:
Now sin =
cos =
tan =
You MUST remember this!!
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Trig ratios on the unit cirlce.
Remember that:
Therefore, from the above diagram; using x, y, and r
if follows that:
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14. 6.1 trignotes.notebook April 01, 2013
HOMEWORK: Pg. 474 #3,4,5,
6 (from Grade 11), 7a), 8, 9,10.
11a)b), Mult. Choice #1,2.
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15. 6.1 trignotes.notebook April 01, 2013
Notice that the size of the circle is NOT important in trig ratios.
.Since the triangle are SIMILAR, the results are the same!
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