Podcast
Questions and Answers
If m∠B is in radians and m∠B = $\frac{\pi}{6}$, what is the measure of the side opposite to this angle in a right triangle?
If m∠B is in radians and m∠B = $\frac{\pi}{6}$, what is the measure of the side opposite to this angle in a right triangle?
What is the measure of the angle in degrees equivalent to $\frac{5\pi}{3}$?
What is the measure of the angle in degrees equivalent to $\frac{5\pi}{3}$?
If $cot(\theta) = 2$, what is the value of $csc(\theta)$?
If $cot(\theta) = 2$, what is the value of $csc(\theta)$?
What is the value of $cos(90^{ ext{o}})$?
What is the value of $cos(90^{ ext{o}})$?
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If $sin(45^{ ext{o}}) = \frac{1}{\sqrt{2}}$, what is the value of $tan(45^{ ext{o}})$?
If $sin(45^{ ext{o}}) = \frac{1}{\sqrt{2}}$, what is the value of $tan(45^{ ext{o}})$?
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What is the value of $sec(0)$?
What is the value of $sec(0)$?
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What is the relationship between $tan(q)$ and $sec(q)$?
What is the relationship between $tan(q)$ and $sec(q)$?
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If an angle q lies in Quadrant IV, what can be said about the coordinates of a point P(x, y) on its terminal side?
If an angle q lies in Quadrant IV, what can be said about the coordinates of a point P(x, y) on its terminal side?
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What is the relationship between $csc(q)$ and $cot(q)$?
What is the relationship between $csc(q)$ and $cot(q)$?
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If an angle q lies in Quadrant II, what can be said about the coordinates of a point P(x, y) on its terminal side?
If an angle q lies in Quadrant II, what can be said about the coordinates of a point P(x, y) on its terminal side?
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If $sec(q) < 0$ and $sin(q) < 0$, which quadrant could q be in?
If $sec(q) < 0$ and $sin(q) < 0$, which quadrant could q be in?
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If cosec q = 5 and the terminal arm of the angle is in Quadrant I, what is the value of cot q?
If cosec q = 5 and the terminal arm of the angle is in Quadrant I, what is the value of cot q?
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What does the word Trigonometry mean?
What does the word Trigonometry mean?
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Which Greek word represents angles in the term Trigonometry?
Which Greek word represents angles in the term Trigonometry?
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How many degrees are in a right angle?
How many degrees are in a right angle?
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If the initial ray rotates in an anti-clockwise direction to coincide with itself, what angle is formed?
If the initial ray rotates in an anti-clockwise direction to coincide with itself, what angle is formed?
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In the sexagesimal system, what unit is used to measure angles?
In the sexagesimal system, what unit is used to measure angles?
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Which branch of Mathematics requires a sound knowledge of Trigonometry?
Which branch of Mathematics requires a sound knowledge of Trigonometry?
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Study Notes
Fundamentals of Trigonometry
- Trigonometry is an important branch of mathematics that deals with the measurement of triangles.
- The word "trigonometry" is derived from three Greek words: "trei" (three), "goni" (angles), and "metron" (measurement).
- Trigonometry is essential for studying calculus and is extensively used in various fields, including business, engineering, surveying, navigation, astronomy, physical, and social sciences.
Sexagesimal System
- The sexagesimal system is used to measure angles in degrees, minutes, and seconds.
- One rotation (anti-clockwise) is equal to 360 degrees (360°).
- A straight angle is equal to 180°, and a right angle is equal to 90°.
Concept of an Angle
- An angle is formed by two rays with a common starting point.
- One of the rays is called the initial side, and the other is called the terminal side.
- The angle is identified by showing the direction of rotation from the initial side to the terminal side.
- Angles can be positive or negative, depending on whether the rotation is anti-clockwise or clockwise.
Units of Measures of Angles
- Angles are usually denoted by Greek letters such as α (alpha), β (beta), γ (gamma), θ (theta), etc.
- The radian is a unit of measurement for angles.
Trigonometric Functions
- The sine, cosine, and tangent of an angle are trigonometric functions.
- The sine, cosine, and tangent of an angle can be defined in terms of the ratios of the sides of a right triangle.
- The trigonometric functions can be positive or negative, depending on the quadrant in which the angle lies.
Quadrant Analysis
- If the angle lies in Quadrant I, then the sine, cosine, and tangent are all positive.
- If the angle lies in Quadrant II, then the sine is positive, and the cosine and tangent are negative.
- If the angle lies in Quadrant III, then the sine and cosine are negative, and the tangent is positive.
- If the angle lies in Quadrant IV, then the sine is negative, and the cosine and tangent are positive.
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Description
Test your knowledge on Quadratic Equations and the Sexagesimal System in Fundamentals of Trigonometry. Explore the basics of trigonometry and its application in measuring triangles.
