Podcast
Questions and Answers
What is the relation between sine and cosine of complementary angles?
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?
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?
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?
Is radius a positive or negative quantity?
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How are the plane quadrants divided by the X and Y axes?
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?
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?
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?
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?
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?
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.
