right triangles and trig ratios
DESCRIPTION
Right Triangles and Trig Ratios. SOH-CAH-TOA. SOH-CAH-TOA is an acronym used in Geometry and Right Triangle Trig to remember what sides of a right triangle go with which Trig Ratios Each angle value (radians and degrees) has a specific ratio of sides that always holds true. - PowerPoint PPT PresentationTRANSCRIPT
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Right Triangles and Trig Ratios
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SOH-CAH-TOA
• SOH-CAH-TOA is an acronym used in Geometry and Right Triangle Trig to remember what sides of a right triangle go with which Trig Ratios
• Each angle value (radians and degrees) has a specific ratio of sides that always holds true
![Page 3: Right Triangles and Trig Ratios](https://reader035.vdocuments.mx/reader035/viewer/2022062301/56812e46550346895d93d69a/html5/thumbnails/3.jpg)
Consider an angle whose terminal ray passes through the point (4, 5)
• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q1)
![Page 4: Right Triangles and Trig Ratios](https://reader035.vdocuments.mx/reader035/viewer/2022062301/56812e46550346895d93d69a/html5/thumbnails/4.jpg)
Consider an angle whose terminal ray passes through the point (-4, 5)
• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q2)
![Page 5: Right Triangles and Trig Ratios](https://reader035.vdocuments.mx/reader035/viewer/2022062301/56812e46550346895d93d69a/html5/thumbnails/5.jpg)
Consider an angle whose terminal ray passes through the point (-4, -5)
• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q3)
![Page 6: Right Triangles and Trig Ratios](https://reader035.vdocuments.mx/reader035/viewer/2022062301/56812e46550346895d93d69a/html5/thumbnails/6.jpg)
Consider an angle whose terminal ray passes through the point (4, -5)
• In which quadrant does this angle fall?• Tell whether the sine, cosine and tangent are
positive or negative for this angle (in Q4)
![Page 7: Right Triangles and Trig Ratios](https://reader035.vdocuments.mx/reader035/viewer/2022062301/56812e46550346895d93d69a/html5/thumbnails/7.jpg)
Trig Definitions/Ratios
• Since the opposite always refers to the vertical distance and the adjacent always refers to the horizontal distance, we can say that…
r
ysin
r
xcos
x
ytan
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Sign Analysis Chart
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Examples
• Tell whether each of the following is positive or negative:
240sin
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Examples
• Tell whether each of the following is positive or negative:
240sin 300cos
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Examples
• Tell whether each of the following is positive or negative:
240sin 300cos
4
3tan
![Page 12: Right Triangles and Trig Ratios](https://reader035.vdocuments.mx/reader035/viewer/2022062301/56812e46550346895d93d69a/html5/thumbnails/12.jpg)
Examples
• Tell whether each of the following is positive or negative:
240sin 300cos
4
3tan
3
4sin
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Finding Exact Values
• If is a 4th quadrant angle and , find and
12
5tan
sin cos
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Finding Exact Values
• An angle has a terminal ray that passes through the point (-4, 7). Find the exact value of the three trig ratios in simplest form.
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The Unit Circle(Quadrantal Angles)
• Consider a circle with radius = ____– What is the sin 90?
– Does the size of the circle matter when evaluating the trig ratios?
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The Unit Circle(Quadrantal Angles)
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Examples
• Find the exact value for each of the following:270sin
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Examples
• Find the exact value for each of the following:270sin 90tan
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Examples
• Find the exact value for each of the following:270sin 90tan
cos
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Examples
• Find the exact value for each of the following:270sin 90tan
cos
2
5sin
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Homework
• Pg. 272 (1 – 27odd)