18 Questions
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?
$\frac{\sqrt{3}}{2}$
What is the measure of the angle in degrees equivalent to $\frac{5\pi}{3}$?
$150^{ ext{o}}$
If $cot(\theta) = 2$, what is the value of $csc(\theta)$?
$-2$
What is the value of $cos(90^{ ext{o}})$?
$0$
If $sin(45^{ ext{o}}) = \frac{1}{\sqrt{2}}$, what is the value of $tan(45^{ ext{o}})$?
$1$
What is the value of $sec(0)$?
$1$
What is the relationship between $tan(q)$ and $sec(q)$?
$tan^2(q) + 1 = sec^2(q)$
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?
Positive x-coordinate and negative y-coordinate
What is the relationship between $csc(q)$ and $cot(q)$?
$csc^2(q) = 1 + cot^2(q)$
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?
Negative x-coordinate and positive y-coordinate
If $sec(q) < 0$ and $sin(q) < 0$, which quadrant could q be in?
Quadrant III
If cosec q = 5 and the terminal arm of the angle is in Quadrant I, what is the value of cot q?
-1/5
What does the word Trigonometry mean?
Measurement of angles
Which Greek word represents angles in the term Trigonometry?
Goni
How many degrees are in a right angle?
90°
If the initial ray rotates in an anti-clockwise direction to coincide with itself, what angle is formed?
360 degrees
In the sexagesimal system, what unit is used to measure angles?
Degree, minute, and second
Which branch of Mathematics requires a sound knowledge of Trigonometry?
Calculus
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.
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.
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