In this lesson we learn:
- Law of sines: Relating angles and opposite sides for any triangle
- Triangulation: Real-world application of the law of sines to find distances
- Law of cosines: Relating three sides and an angle for any triangle
- Triangle area (SAS): Find a triangle's area using 2 sides and the angle between
Triangle has sides of lengths a, b, and c opposite the angles A, B, and C then:
a/sin A = b/sin B = c/sin C
Triangle has sides of lengths a, b, and c opposite the angles A, B, and C then:
c^2 = a^2 + b^2 − 2ab cos C
Less effort more effective
Showing posts with label Trigonometry. Show all posts
Showing posts with label Trigonometry. Show all posts
Trig Identities
In this lesson we learn:
- Trig identities: The tools for simplifying trig expressions
- Addition identities: Simplify trig functions of sums
- Negative angle identities: Simplify trig functions of negative angles
- Subtraction identities: Simplify trig functions of differences
- Double angle identities: Trig functions of twice an angle
- Triple angle identities: Trig functions of three times an angle
- Pythagorean identities: Relating squares of trig functions
- Half angle identities: Trig functions of half an angle
sin(2a) = sin(a+a) = sin(a) cos(a) + cos(a) sin (a) = 2 sin(a) cos(a)
- Trig identities: The tools for simplifying trig expressions
- Addition identities: Simplify trig functions of sums
- Negative angle identities: Simplify trig functions of negative angles
- Subtraction identities: Simplify trig functions of differences
- Double angle identities: Trig functions of twice an angle
- Triple angle identities: Trig functions of three times an angle
- Pythagorean identities: Relating squares of trig functions
- Half angle identities: Trig functions of half an angle
sin(2a) = sin(a+a) = sin(a) cos(a) + cos(a) sin (a) = 2 sin(a) cos(a)
Inverse sine - Inverse cosine - Inverse tangent | Inverse Trig Functions
In this lesson we learn:
- Inverse sine: A function that takes you from side ratios to angles
- Inverse cosine: Another inverse trig function
- Inverse tangent: And one last inverse trig function!
Inverse sine function y = sin−1(x) or sometimes called the arc sine and denoted by y = arcsin(x) whose domain is the interval [−1,1] and whose range is the interval [-Pi/2, Pi/2].
The inverse cosine function y = cos−1(x) or we can called the arc cosine and denoted by y = arccos(x) can be determined in a similar fashion. The function y = cos(x) is one-to-one over the interval [0,Pi].
The inverse tangent function y = tan−1(x) or we can called the arc tangent and denoted by y = arctan(x) can be determined similarly. The function y = tan(x) is one-to-one over the interval (-Pi/2, Pi/2)
- Inverse sine: A function that takes you from side ratios to angles
- Inverse cosine: Another inverse trig function
- Inverse tangent: And one last inverse trig function!
Inverse sine function y = sin−1(x) or sometimes called the arc sine and denoted by y = arcsin(x) whose domain is the interval [−1,1] and whose range is the interval [-Pi/2, Pi/2].
The inverse cosine function y = cos−1(x) or we can called the arc cosine and denoted by y = arccos(x) can be determined in a similar fashion. The function y = cos(x) is one-to-one over the interval [0,Pi].
The inverse tangent function y = tan−1(x) or we can called the arc tangent and denoted by y = arctan(x) can be determined similarly. The function y = tan(x) is one-to-one over the interval (-Pi/2, Pi/2)
The Unit Circle - Trigonometry
This lesson we learn:
- Trig for larger angles: What's sin(250)? Use the unit circle to tackle bigger angles
- Trig for negative angles: Using the unit circle for trig with negative angles
- Trig for coterminals: How trig functions are related for coterminal angles.
The unit circle has coordinates (x, y) which x-axis as cos(θ) and y-axis as sin(θ), where θ is the angle that the line segment from the origin to (x, y) makes with the positive x-axis and the point (x, y) goes around the circle, its y-coordinate is sin θ.
The counter-clockwise rotation angle is positive, and the angle is negative when the rotation is clockwise.
Coterminal angles differ by an integer multiple of 360 degrees then each trigonometric function will have equal values at both angles, which have the same initial and terminal sides.
- Trig for larger angles: What's sin(250)? Use the unit circle to tackle bigger angles
- Trig for negative angles: Using the unit circle for trig with negative angles
- Trig for coterminals: How trig functions are related for coterminal angles.
The unit circle has coordinates (x, y) which x-axis as cos(θ) and y-axis as sin(θ), where θ is the angle that the line segment from the origin to (x, y) makes with the positive x-axis and the point (x, y) goes around the circle, its y-coordinate is sin θ.
The counter-clockwise rotation angle is positive, and the angle is negative when the rotation is clockwise.
Coterminal angles differ by an integer multiple of 360 degrees then each trigonometric function will have equal values at both angles, which have the same initial and terminal sides.
Special Angles - 45 degrees - 30/60 degrees - 0/90 degrees - Trigonometry
In this article we are going to learn:
- 45 degrees: Calculate the sine, cosine, and tangent of 45 degrees
- 30/60 degrees: Calculate the sine, cosine, and tangent of 30 and 60 degrees
- 0/90 degrees: Calculate the sine, cosine, and tangent of 0 and 90 degrees
An isosceles triangle is a triangle with two sides of equal length
In a right triangle, the side opposite of the right angle is called the hypotenuse, and the other two sides are called its legs(or called opposites, adjacent).
Sine = opposites side / hypotenuses
Cosine = adjacent side / hypotenuse
Tan = opposites / adjacent
Sec() = 1/cos() or hypotenuse/adjacent
Csc() = 1/sin() or hypotenuse/opposite
Cot() = 1/tan() or cos()/sin() or adjacent/opposite
- 45 degrees: Calculate the sine, cosine, and tangent of 45 degrees
- 30/60 degrees: Calculate the sine, cosine, and tangent of 30 and 60 degrees
- 0/90 degrees: Calculate the sine, cosine, and tangent of 0 and 90 degrees
An isosceles triangle is a triangle with two sides of equal length
In a right triangle, the side opposite of the right angle is called the hypotenuse, and the other two sides are called its legs(or called opposites, adjacent).
Sine = opposites side / hypotenuses
Cosine = adjacent side / hypotenuse
Tan = opposites / adjacent
Sec() = 1/cos() or hypotenuse/adjacent
Csc() = 1/sin() or hypotenuse/opposite
Cot() = 1/tan() or cos()/sin() or adjacent/opposite
Trigonometry – Trig Functions
In this lesson we going to learn:
- Sides of right triangles: Your friendly hypotenuses, opposites, and adjacent- Sine: Your very first trig function
- Cosine: Along with sine, cosine is a fundamental trig function- Tangent: Another important trig function (like sine and cosine)- Components (and cops): Find legs of right triangles, and don't get pulled over!- Sec, Csc, and Cot: Secant and friends (three more trig functions)
In a right triangle, the side opposite of the right angle is called the hypotenuse, and the other two sides are called its legs.
Sine = opposites side / hypotenuses
Cosine = adjacent side / hypotenuse
Tan = opposites / adjacent
Sec() = 1/cos() or hypotenuse/adjacent
Csc() = 1/sin() or hypotenuse/opposite
Cot() = 1/tan() or cos()/sin() or adjacent/opposite
- Sides of right triangles: Your friendly hypotenuses, opposites, and adjacent- Sine: Your very first trig function
- Cosine: Along with sine, cosine is a fundamental trig function- Tangent: Another important trig function (like sine and cosine)- Components (and cops): Find legs of right triangles, and don't get pulled over!- Sec, Csc, and Cot: Secant and friends (three more trig functions)
In a right triangle, the side opposite of the right angle is called the hypotenuse, and the other two sides are called its legs.
Sine = opposites side / hypotenuses
Cosine = adjacent side / hypotenuse
Tan = opposites / adjacent
Sec() = 1/cos() or hypotenuse/adjacent
Csc() = 1/sin() or hypotenuse/opposite
Cot() = 1/tan() or cos()/sin() or adjacent/opposite
Trigonometry – Radians
In this lesson we will learn:
Radians to degrees: x radians = (180/Pi time x) degrees
Circular arc is part of a circle’s circumference between two radii.
Sector is part of a circle between two radii.
- What's a radian? Discover another way to measure angles.
- Radians and degrees: How to switch back and forth between units for angles
- Lengths of circular arcs: A formula for arc length in terms of radius and angle
- Sectors: Learn what a sector is, and a formula for finding its area
Radians to degrees: x radians = (180/Pi time x) degrees
Circular arc is part of a circle’s circumference between two radii.
Sector is part of a circle between two radii.
Subscribe to:
Posts (Atom)