Questions and Answers
What is the term for 'Sine'?
Sine
What is the term for 'Cosine'?
Cosine
What is the term for 'Tangent'?
Tangent
What is the value of 'Sine 30'?
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What is the value of 'Sine 60'?
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What is the value of 'Sine 45'?
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What is the value of 'Cos 30'?
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What is the value of 'Cos 60'?
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What is the value of 'Cos 45'?
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What is the value of 'Tan 30'?
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What is the value of 'Tan 60'?
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What is the value of 'Tan 45'?
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What does 'Standard Position' refer to?
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What is the 'Initial Side' of an angle?
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What is the 'Terminal Side' of an angle?
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What are 'Coterminal Angles'?
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What is a 'Reference Angle'?
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What is a 'Radian'?
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What is the conversion from degrees to radians?
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What is the conversion from radians to degrees?
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What is a 'Unit Circle'?
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What is the 'Arc Length Formula'?
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What are 'Inverse Trig Functions'?
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What is the 'Area of A Triangle' formula?
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What is the 'Law of Sines'?
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What is the 'Law of Cosines'?
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What is 'Heron's Formula'?
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What are 'Transformation of Sin & Cos Graphs'?
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What are 'Transformation of Tangent Graphs'?
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What are 'Transformation of Cotangent Graphs'?
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What are 'Reciprocal Identities'?
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What are 'Tangent and Cotangent Ratio Identities'?
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What are 'Pythagorean Identities'?
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What are 'Negative-Angle Identities'?
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What are 'Sum and Difference Identities'?
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What are 'Double Angle Identities'?
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What are 'Half Angle Identities'?
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Study Notes
Sine, Cosine, and Tangent
- Sine: A trigonometric function defined as the ratio of the length of the opposite side to the hypotenuse in a right triangle.
- Cosine: Defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle.
- Tangent: The ratio of the sine to the cosine, or equivalently, the ratio of the opposite side to the adjacent side in a right triangle.
Key Sine Values
- Sine 30: Equals 1/2.
- Sine 60: Equals √3/2.
- Sine 45: Equals √2/2.
Key Cosine Values
- Cosine 30: Equals √3/2.
- Cosine 60: Equals 1/2.
- Cosine 45: Equals √2/2.
Key Tangent Values
- Tangent 30: Equals √3/3.
- Tangent 60: Equals √3.
- Tangent 45: Equals 1.
Angle Definitions
- Standard Position: An angle positioned with its vertex at the origin and one ray along the positive x-axis.
- Initial Side: The side of an angle that lies along the x-axis in standard position.
- Terminal Side: The ray that results from the rotation of the initial side.
Special Angle Concepts
- Coterminal Angles: Angles that share the same terminal side when in standard position; can be obtained by adding or subtracting multiples of 360° or 2π radians.
- Reference Angle: The smallest positive angle formed between the terminal side of an angle and the x-axis.
Unit of Measure
- Radian: A unit of angular measure based on the radius of a circle used primarily in trigonometry.
- Degrees to Radians: Conversion requires multiplying degrees by π/180.
- Radians to Degrees: Conversion requires multiplying radians by 180/π.
Key Trigonometric Concepts
- Unit Circle: A circle with a radius of one, used to define trigonometric functions.
- Arc Length Formula: Relates the angle in radians and the radius to find the length of the arc.
Areas and Laws
- Area of a Triangle: Can be calculated using various formulas depending on known variables.
- Law of Sines: Relates the ratios of the lengths of sides of a triangle to the sines of the corresponding opposite angles.
- Law of Cosines: Relates the lengths of sides of a triangle to the cosine of one of its angles.
- Heron’s Formula: Calculates the area of a triangle when the lengths of all three sides are known.
Graph Transformations
- Transformation of Sin & Cos Graphs: Involves stretching, compressing, or shifting the sine and cosine functions.
- Transformation of Tangent Graphs: Similar transformations apply but will modify the periodic behavior.
- Transformation of Cotangent Graphs: Affects the position and shape of the cotangent function graph.
Trigonometric Identities
- Reciprocal Identities: Define relationships between the primary trigonometric functions and their reciprocals.
- Tangent and Cotangent Ratio Identities: Establish relationships between tangent, cotangent, sine, and cosine.
- Pythagorean Identities: Derived from the Pythagorean theorem and relate the squares of sine, cosine, and tangent.
- Negative-Angle Identities: Allow calculations of functions of negative angles.
- Sum and Difference Identities: Enable the calculation of trigonometric functions for the sum or difference of angles.
- Double Angle Identities: Provide formulas to express trigonometric functions of double angles.
- Half Angle Identities: Provide formulas for trigonometric functions of half angles.
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Test your knowledge of trigonometric functions with these flashcards. Each card covers key terms and values related to sine and cosine, including specific angles. Perfect for students looking to reinforce their understanding of trigonometry in Algebra 3.