Chapter 7 - Trigonometry
Prescribed Learning Outcomes:
B1 Solve problems by using the sine law and cosine law, excluding the ambiguous case.
B1 Solve problems by using the sine law and cosine law, excluding the ambiguous case.
Chapter 7 key ideas
- Use the primary trigonometric ratios (sine, cosine, and tangent) to find the measure of a side or an angle in a right triangle.
- Use the sine law to find the measure of a side or an angle in a non-right triangle.
- Use the cosine law to find the measure of a side or an angle in a non-right triangle.
Trigonometry Review
If necessary, watch the trigonometry review video from chapter 5 to ensure that you are able to use the sine, cosine, and tangent ratios to find the measure of a side or an angle in a right triangle. Do page 258 #1-2.
7.1 The Sine Law
The sine and cosine laws enable us to use trigonometry in triangles that do not contain a right triangle. They can be used to find the length of a side or the measure on an angle. Either the sine law will work or the cosine law will work in a problem, not both.
The sine law works when you know
Remember, if you know two angles you can calculate the third by subtracting the two angles from 180 so the second bullet works if you know two angles and ANY side.
Watch the sine law video and then do page 262 #3, page 264 #4, and page 266 #5-7.
The sine law works when you know
- two sides and the angle opposite one of them, or
- two angles and the side opposite one of them
Remember, if you know two angles you can calculate the third by subtracting the two angles from 180 so the second bullet works if you know two angles and ANY side.
Watch the sine law video and then do page 262 #3, page 264 #4, and page 266 #5-7.
7.2 The Cosine Law
Remember, the cosine law will work when the sine law will not work.
The cosine law works when you know
In some complex problems, you may have to use both the sine law and the cosine law to find different pieces of information.
Watch the cosine law video and do page 276 #1-3, page 279 #4-6, page 282 #7-9, and page 284 #1-4.
The cosine law works when you know
- two side and the angle between them, or
- all three sides
In some complex problems, you may have to use both the sine law and the cosine law to find different pieces of information.
Watch the cosine law video and do page 276 #1-3, page 279 #4-6, page 282 #7-9, and page 284 #1-4.
Review for this chapter:
Read the key ideas at the top of this page and ensure that you understand them all.
Mark all of your homework with the answer key in the classroom.
Complete and mark the practice test on page 287.
Mark all of your homework with the answer key in the classroom.
Complete and mark the practice test on page 287.