## Podcast Beta

## Questions and Answers

What does one complete revolution equal?

What are the degrees of an acute angle?

less than 90 degrees

What are the degrees of a right angle?

90 degrees

What are the degrees of an obtuse angle?

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What are the degrees of a straight angle?

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If two angles have a sum of 90 degrees, what are they called?

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If two angles have a sum of 180 degrees, what are they called?

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What is the equation for the complementary angle?

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What is the equation for the supplementary angle?

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What does a little line (tick) mean if it's going through a line of a triangle?

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Where are the legs a, b, hypotenuse c, and theta located in a right triangle?

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What is the equation for the Pythagorean theorem?

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What are the degrees for a special triangle that has equal sides?

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What is the ratio of a 30-60-90 triangle?

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What are the two types of special triangles in degrees?

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What is the ratio for a 45-45-90 degree triangle?

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What is the vertex of a square?

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Where are the first, second, third, and fourth quadrants located on a graph?

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What is the distance formula?

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What letters signify the center point and what letter signifies the radius when finding the equation of a circle?

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What are the trigonometric functions?

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What formula do we use to find the remaining trigonometric functions?

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The reciprocal identities include 1/cosθ = secθ.

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What are the ratio identities?

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What is the rule to memorize the signs of trigonometric functions in a given quadrant?

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## Study Notes

### Basic Angle Measurements

- One complete revolution is 360 degrees.
- Acute angles measure less than 90 degrees.
- Right angles measure exactly 90 degrees.
- Obtuse angles measure greater than 90 degrees but less than 180 degrees.
- Straight angles measure 180 degrees.

### Angle Relationships

- Complementary angles sum up to 90 degrees.
- Supplementary angles sum up to 180 degrees.
- Complementary and supplementary formulas: 90 - y and 180 - y respectively.

### Triangle Properties

- Tick marks on triangle sides indicate length differences (one tick means equal length, different ticks indicate varied lengths).
- In a right triangle:
- Hypotenuse (c) is the longest side.
- Leg a is the bottom side, leg b is the left side.
- Theta (θ) is located at the angle inside the triangle.

### Pythagorean Theorem

- The formula is a² + b² = c², where c is the hypotenuse.

### Special Triangles

- Equilateral triangles have three equal sides and angles: 60°, 60°, 60°.
- A 30-60-90 triangle has angles of 30°, 60°, and 90° with side ratios t : √3t : 2t.
- A 45-45-90 triangle has angles of 45°, 45°, and 90° with side ratios t : t : √2t.

### Graphing Coordinates

- First Quadrant (top right): x and y are positive.
- Second Quadrant (top left): x is negative, y is positive.
- Third Quadrant (bottom left): x and y are negative.
- Fourth Quadrant (bottom right): x is positive, y is negative.

### Distance and Circle Formulas

- Distance formula: √[(x₂ - x₁)² + (y₂ - y₁)²].
- Circle equation center is at (h,k) with radius r: (x - h)² + (y - k)² = r².

### Trigonometric Functions

- Sine: sin(θ) = y/r
- Cosine: cos(θ) = x/r
- Tangent: tan(θ) = y/x
- Secant: sec(θ) = r/x
- Cosecant: csc(θ) = r/y
- Cotangent: cot(θ) = x/y.

### Finding Trigonometric Functions

- To find remaining trig functions, use r² = x² + y² (derived from the Pythagorean theorem).

### Identities in Trigonometry

- Reciprocal identities:
- cscθ = 1/sinθ
- secθ = 1/cosθ
- cotθ = 1/tanθ

- Ratio identities:
- cotθ = x/y = cosθ/sinθ
- tanθ = sinθ/cosθ.

### CAST Rule

- Used to memorize signs of trigonometric functions in different quadrants:
- C (cos) in the fourth quadrant is positive.
- A (All) in the first quadrant means all functions are positive.
- S (sin) in the second quadrant is positive.
- T (tan) in the third quadrant is positive.

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## Description

Test your knowledge on basic angle measurements and properties of triangles. This quiz covers the types of angles, relationships between them, and the Pythagorean theorem. Perfect for students studying geometry or anyone looking to refresh their math skills.