Questions and Answers
An angle that is in standard position has its vertex at the origin and its initial side on the positive x-axis.
True
The sine of an angle on the Cartesian plane can be found by using the formula x/r.
False
The legs in a 30°-60°-90° triangle are equal.
False
A standard position angle whose terminal side falls on the x-axis or y-axis is called a quadrantal angle.
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What is the length of the hypotenuse in a 30°-60°-90° triangle?
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What is the length of the long leg in a 30°-60°-90° triangle?
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What is the length of the hypotenuse in a 30°-45°-90° triangle?
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What is the length of the leg in a 30°-45°-90° triangle?
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What is the value of tanθ for an angle in standard position passing through (6, 8)?
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What is the value of cosθ for an angle in standard position passing through (6, 8)?
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Study Notes
Angle Measurement and Properties
- An angle in standard position has its vertex at the origin with the initial side on the positive x-axis.
- A quadrantal angle has its terminal side along the x-axis or y-axis.
Trigonometric Functions
- The sine of an angle is not represented by x/r; the correct relationship is sine = y/r.
- Cosine is the correct term for the ratio x/r in trigonometric identities.
Special Triangles
- In a 30°-60°-90° triangle, the sides are in the ratio 1:√3:2; the hypotenuse is twice the length of the shorter leg.
- For a 30°-45°-90° triangle, the sides are in the ratio 1:1:√2; the legs are equal, and the hypotenuse is √2 times the leg length.
Triangle Side Lengths
- For a 30°-60°-90° triangle, if the hypotenuse is 6, the long leg measures 3√3.
- In a 30°-45°-90° triangle with a hypotenuse of 4√2, each leg measures 4.
Trigonometric Values
- For an angle in standard position passing through the point (6, 8):
- The tangent function is calculated as tanθ = opposite/adjacent = 8/6 = 4/3.
- The cosine function value for this angle is cosθ = adjacent/hypotenuse = 6/√(6² + 8²) = 3/5.
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Test your knowledge with these flashcards for Abeka Algebra II Quiz 29. This quiz covers key concepts and definitions related to angles, trigonometric functions, and triangle properties. Perfect for reinforcing your understanding before your next test!
