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Questions and Answers
What is the relation between sine and cosine of complementary angles?
sine (90 degrees - theta) = cos theta, cos (90 degrees - theta) = sine theta
What are the trigonometric ratios of sine and cosine?
sine theta = opposite / hypotenuse, cos theta = adjacent / hypotenuse
In which quadrants are sine and cosine positive and negative?
Sine and cosine are positive in first and second quadrants, negative in third and fourth
Is radius a positive or negative quantity?
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How are the plane quadrants divided by the X and Y axes?
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What is the relation between sine and cosine through Pythagorean theorem?
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How can rotation angles in degrees be converted into radians?
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What are the specific values of sine and cosine at certain angles?
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How can the value of theta be found using trigonometric functions?
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What can trigonometric functions be used to find in right triangles?
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Study Notes
- Trigonometric ratios are complementary: sine (90 degrees - theta) = cos theta, cos (90 degrees - theta) = sine theta
- Sine and cosine are ratios of length: sine theta = opposite / hypotenuse, cos theta = adjacent / hypotenuse
- Trigonometric functions involve angles in quadrants: sine and cosine are positive in first and second quadrants, negative in third and fourth
- Radius is a scalar quantity, always positive
- X and Y axes divide the plane into quadrants, null quadrants also exist
- Sine and cosine are related through Pythagorean theorem: sine^2 theta + cos^2 theta = 1
- Trigonometric functions can be used to find angles in various quadrants, using complementary angles and the Pythagorean theorem.
- Rotation angles in degrees can be converted into radians: 180 degrees = π radians, 360 degrees = 2π radians.
- Trigonometric functions have specific values at certain angles: sine 30 degrees = 0.5, cos 30 degrees = 0.866, sine 45 degrees = 0.707, cos 45 degrees = 0.707.
- Theta value can be found using trigonometric functions: sine theta = opposite / hypotenuse, cos theta = adjacent / hypotenuse, tan theta = opposite / adjacent.
- The given text mentions several specific angles and their corresponding trigonometric values.
- Trigonometric functions can be used to find missing sides or angles in right triangles.
- Trigonometric functions can be used to find the angle of elevation or depression.
- Trigonometric functions can be used to find the period and amplitude of a sinusoidal wave.
- Trigonometric functions can be used to find the phase shift and vertical shift of a sinusoidal wave.
- Trigonometric functions can be used to find the equation of a circle.
- Trigonometric functions can be used in various applications, such as engineering, physics, and mathematics.
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Description
Test your knowledge of trigonometric functions, their properties, specific angles, applications in solving triangles, and their applications in various fields such as engineering, physics, and mathematics.
