For any right triangle
Define the sine, cosine, and tangent ratios and their inverses
Find the measure of a side given a side and an angle
Find the measure of an angle given two sides
Use trig ratios to solve problems
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
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Obj. 40 Trigonometry
1. Obj. 40 Trigonometry
The student is able to (I can):
For any right triangle
âą Define the sine, cosine, and tangent ratios and their
inverses
âą Find the measure of a side given a side and an angle
âą Find the measure of an angle given two sides
âą Use trig ratios to solve problems
2. By the Angle-Angle Similarity Theorem, a
right triangle with a given acute angle is
similar to every other right triangle with the
same acute angle measure. This means
that the ratios between the sides of those
triangles are always the same.
Because these ratios are so useful, they
were given names: sine cosine and
sine, cosine,
tangent.
tangent These ratios are used in the
study of trigonometry.
4. We can use the trig ratios to find either
missing sides or missing angles of right
triangles. To do this, we will set up
equations and solve for the missing part.
In order to figure out the sine, cosine, and
tangent ratios, we can use either a
calculator or a trig table.
5. To use the calculator to find tan 51°:
⹠From a New Document, press the ” key:
âą Use the right arrow key ( ) to select tan
(Âą)
and press ·:
6. ⹠Type 5I and hit ·:
To use the calculator on your phone:
âą Turn your phone landscape to access
the scientific calculator.
âą Type the angle in first, then select sin.
7. To use the trig table to find cos 52°:
⹠Locate 52° on the table.
âą Scan over to the Cos column and find
the value.
⹠cos 52° = .6157
8. You will be expected to memorize these
ratios. There are many hints out there to
help you keep them straight. The most
common is SOH-CAH-TOA , where
SOH-CAHOp p
Sin =
Hyp
Adj
Cos =
Hyp
Op p
Tan =
Adj
A mnemonic I like is âSome Old Hippie
Caught Another Hippie Trippinâ On Acid.â
Or âSilly Old Hitler Couldnât Advance His
Troops Over Africa.â
9. Examples
I.
Use the triangle to find the following
ratios.
A
8
C
1.
sin A = _____
2. cos A = _____
3. tan A = _____
17
B
15
10. Examples
I.
Use the triangle to find the following
ratios.
A
8
1.
15
17
sin A = _____
8
17
2. cos A = _____
15
8
3. tan A = _____
C
17
B
15
11. Examples
I.
Use the triangle to find the following
ratios.
A
8
C
4. sin B = _____
5. cos B = _____
6. tan B = _____
17
B
15
12. Examples
I.
Use the triangle to find the following
ratios.
A
8
8
17
4. sin B = _____
15
17
5. cos B = _____
8
15
6. tan B = _____
C
17
B
15
13. Examples
II.
Find the lengths of the sides to the
nearest tenth.
x (opp)
1.
15
(adj)
58°
x
sin58° =
15
x = 15sin58°
â 12.7
2.
x
26
x = 26cos 46°
cos 46° =
26
(hyp)
46°
x
(adj)
â 18.1