Questions and Answers
How many radians are there in 360 degrees?
2π
What are the sides of a 45-45-90 triangle?
Hypotenuse = 1, other sides = √½
How do you complete the square?
What kind of symmetry does a cosine function have?
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What kind of symmetry does a sine function have?
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How do you find an inverse function?
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Why are reference angles useful?
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What is the definition of a reference angle?
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How do you know if a trig identity is positive or negative in a given quadrant?
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How do you find the coordinates of a point on a unit circle according to its angle or reference angle?
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What's the formula for standard deviation using population proportions?
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What's the formula for standard deviation using sample means?
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What is the probability of getting 2 heads in a row?
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What is another term for 'percent rate of change'?
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What is the definition of a parabola?
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Study Notes
Radians and Degrees
- 360 degrees is equivalent to 2π radians.
- In a unit circle, the circumference is C=2π, which also represents 360 degrees.
45-45-90 Triangle
- The hypotenuse measures 1 (radius of a unit circle).
- The lengths of the other two sides are both √½, derived using the Pythagorean theorem.
Completing the Square
- A method used to convert a quadratic equation into a perfect square trinomial for easier solving.
Symmetry in Functions
- The cosine function exhibits y-axis symmetry, allowing reflection of quadrants 2 and 3 across the y-axis to quadrants 1 and 4.
- The sine function is symmetric with respect to the origin, permitting a 180-degree rotation of quadrants 2 and 3 to quadrants 4 and 1.
Inverse Functions
- Finding an inverse function typically involves swapping the input and output values in the equation and solving for the new output.
Reference Angles
- Useful for determining trigonometric identities as an angle and its reference angle share the same sine, cosine, and tangent values.
- Positive or negative signs of these trigonometric values may vary depending on the quadrant.
Definition of Reference Angle
- The smallest angle formed by the terminal side of an angle with the x-axis.
Trigonometric Identity Signs
- Memorization tool: "All Strippers Take Cash" indicates which trigonometric ratios are positive in each quadrant.
Coordinates on the Unit Circle
- Coordinates based on angle or reference angle determined via cosine and sine values, represented as (cosine, sine).
- The order of cosine before sine aligns with their alphabetical arrangement.
Standard Deviation Formulas
- For population proportions, the formula is represented as p (population proportion).
- For sample means, σ represents sample standard deviation, with σ sub x denoting standard deviation.
Probability of Coin Flips
- The probability of flipping 2 heads consecutively is calculated as (1/2)(1/2) = 1/4.
- The first flip's success rate is 50%, and the same applies to the second flip, leading to a combined chance of 1/4.
Percent Rate of Change
- Also referred to as the growth or decay factor, capturing the rate of change in percentage terms.
Definition of a Parabola
- A parabola is defined as the set of all points where the distance to a fixed point (focus) equals the distance to a fixed line (directrix).
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Description
Test your knowledge on radians, degrees, and the properties of triangles including 45-45-90 triangles. Explore concepts such as completing the square, function symmetry, inverse functions, and reference angles. This quiz is essential for mastering trigonometry and quadratic equations.
