Podcast
Questions and Answers
What is the relationship expressed by the Pythagorean theorem in a right triangle?
What is the relationship expressed by the Pythagorean theorem in a right triangle?
- a² = b² + c²
- a² + b² = c
- a + b = c
- a² + b² = c² (correct)
In a 30-60-90 triangle, what is the ratio of the sides?
In a 30-60-90 triangle, what is the ratio of the sides?
- 1:1:2
- 1:2:√3
- 1:√3:2 (correct)
- √3:1:2
Which function corresponds to the ratio of opposite to adjacent in a right triangle?
Which function corresponds to the ratio of opposite to adjacent in a right triangle?
- Tangent (correct)
- Sine
- Cosecant
- Secant
How would you find the angle if you know the ratio of the opposite side to the hypotenuse?
How would you find the angle if you know the ratio of the opposite side to the hypotenuse?
Which of these is NOT a special right triangle?
Which of these is NOT a special right triangle?
Which of the following topics is NOT included in the trigonometry course?
Which of the following topics is NOT included in the trigonometry course?
What formula would be used to convert an angle measured in degrees, minutes, and seconds (DMS) to radians?
What formula would be used to convert an angle measured in degrees, minutes, and seconds (DMS) to radians?
Which trigonometric function is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle?
Which trigonometric function is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle?
What is the purpose of the sum and difference formulas in trigonometry?
What is the purpose of the sum and difference formulas in trigonometry?
Which method would be used to verify a trigonometric identity?
Which method would be used to verify a trigonometric identity?
Flashcards
Hypotenuse
Hypotenuse
The side opposite the right angle in a right triangle.
SOH CAH TOA
SOH CAH TOA
A mnemonic device to remember the trigonometric ratios: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.
30-60-90 Triangle
30-60-90 Triangle
A right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees, and sides in the ratio 1:√3:2.
45-45-90 Triangle
45-45-90 Triangle
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Trigonometry
Trigonometry
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Sine (sin)
Sine (sin)
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Cosine (cos)
Cosine (cos)
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Tangent (tan)
Tangent (tan)
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Law of Sines
Law of Sines
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Law of Cosines
Law of Cosines
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Study Notes
Right Triangle trigonometry
- Trigonometry studies relationships between triangle sides and angles.
- In right triangles, the hypotenuse is opposite the right angle.
- The Pythagorean theorem: a² + b² = c² (hypotenuse squared equals sum of other two sides squared).
- Six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), cotangent (cot).
- SOH CAH TOA:
- Sine = Opposite / Hypotenuse
- Cosine = Adjacent / Hypotenuse
- Tangent = Opposite / Adjacent
- Reciprocals:
- Cosecant (csc) = 1/sin
- Secant (sec) = 1/cos
- Cotangent (cot) = 1/tan
- Special right triangles: 3-4-5, 5-12-13, 8-15-17, 7-24-25, multiples of these are also special.
- Less common special right triangles: 9-40-41, 11-60-61
- Pythagorean theorem used to find missing sides.
- SOH CAH TOA used for finding trigonometric function values.
- Inverse trigonometric functions used to find missing angles: arcsin (sin⁻¹), arccos (cos⁻¹), arctan (tan⁻¹).
Special Triangles
- 30-60-90 Triangle: Side ratio 1:√3:2.
- 45-45-90 Triangle: Side ratio 1:1:√2.
Trigonometry Course
- Udemy course covers:
- Angles, radians, co-terminal angles, DMS conversions, arc length, sector area, linear/angular speed
- Unit circle, six trig functions, reference angles
- Right triangle trig, solving for missing sides/angles
- Trig functions of any angle
- Graphing trig functions
- Inverse trig functions
- Composite trig functions
- Applications (two right triangles, bearings)
- Verifying trig identities
- Sum/difference formulas, double/half-angle, power-reducing, product-to-sum/sum-to-product formulas
- Solving trig equations
- Law of sines, law of cosines, polar coordinates, further topics.
- Course is ongoing, adding more sections.
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Description
Test your knowledge of right triangle trigonometry concepts. This quiz covers the fundamentals, including the Pythagorean theorem, special right triangles, and trigonometric ratios. Perfect for students learning trigonometry principles!
