Definition of Trigonometric Ratios. The six trigonometric ratios relate the sides of a right triangle to its angles. Specifically, they are ratios of two sides of a right triangle and a related angle. Trigonometric functions are typically used to calculate unknown lengths or angles in a right triangle. The six functions are all related and can be defined in terms of one another.
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Sin, Cos, Tan. We've had our fun with triangles and legs, Pythagoras and his invention, and exponentials and square roots. But seriously, that stuff isn't at the core of trig. Real trig rocks to the tune of sin, cos, and tan.
http://www.shmoop.com/trig-functions/trig-ratios.html
Trigonometric and Triangle Identities. And as you get better at Trigonometry you can learn these: The Trigonometric Identities are equations that are true for all right-angled triangles. The Triangle Identities are equations that are true for all triangles (they don't have to have a right angle).
https://www.mathsisfun.com/algebra/trigonometry.html
Sample Problem. If a = 1 and b = 1, find sin, cos, and tan of angle A. First find c. c 2 = 1 2 + 1 2 c 2 = 1 + 1. c 2 = 2. Now just take the square root of both sides. Now applying the trig ratios. Hint: Don't forget to rationalize your denominators. For a refresher on this little calculation, go here.
http://www.shmoop.com/trig-functions/trig-ratios.html
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https://www.ixl.com/math/geometry/trigonometric-ratios-sin-cos-and-tan
Problem 2: In the figure below, find c. Detailed Solution. Problem 3: If x is an acute angle of a right triangle and sin x = 3 / 7, find the exact value of the trigonometric functions cos x and cot x. Detailed Solution. Problem 4: Find the exact values of x and y. Detailed Solution.
http://www.analyzemath.com/Trigonometry_problems/trigonometric_ratios.html
The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner. We usually know another angle θ. And we give names to each side: 1  Adjacent is adjacent (next to) to the angle θ. 2  Opposite is opposite the angle θ. 3  the longest side is the Hypotenuse.
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Cotangent. cot. The ratios for the three main functions — sine, cosine, and tangent — can be recalled using the acronym SOHCAHTOA. When applied to a right triangle inscribed within the unit circle with the hypotenuse equal to the radius of the circle, , , and.
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Sine, Cosine and Tangent. Trigonometry is good at find a missing side or angle in a triangle. The special functions Sine, Cosine and Tangent help us! They are simply one side of a right-angled triangle divided by another.
https://www.mathsisfun.com/algebra/trigonometry.html
A set of problems, that may be solved using the trigonometric ratios, is presented. Also detailed solutions are presented in a separate page. Definition of Trigonometric Ratios. Problem 1: Given the right triangle below, find. sin A, cos A, tan A, sec A, csc A and cot A. Detailed Solution.
http://www.analyzemath.com/Trigonometry_problems/trigonometric_ratios.html
what are trigonometric ratios
The six trigonometric ratios relate the sides of a right triangle to its angles. Specifically, they are ratios of two sides of a right triangle and a related angle.