Sin, Cos and Tan for Larger Angles

Sin, Cos and Tan for Larger Angles

  • Sin, Cos and Tan Functions: Remember they denote the ratio of sides in a right-angled triangle. For an angle A, Sin A is the ratio of the length of the side opposite angle A to the hypotenuse, Cos A is the length of the adjacent side to hypotenuse, and Tan A is the opposite side to adjacent side.

  • Quadrants: For angles between 90 and 360 degrees, they lie in one of the quadrants II, III, or IV. In quadrant II, Sin is positive, Cos and Tan are negative. In quadrant III, Tan is positive, Sin and Cos are negative. In quadrant IV, Cos is positive, Sin and Tan are negative.

  • Finding Exact Values: Exact values for Sin, Cos and Tan can be found for angles of 0°, 30°, 45°, 60° and 90°. Remember these special angles as they come in handy.

  • Sin, Cos and Tan graphs: The graphs of these functions can help understand their behaviour. Sin and Cos graphs repeat every 360 degrees, while Tan graph repeats every 180 degrees.

  • 180 and 360 Degrees: For Sin, Cos and Tan, remember that Sin(180 - A) = Sin A, Cos(180 - A) = -Cos A, and Tan(180 - A) = -Tan A. Similarly, Sin(360 - A) = -Sin A, Cos(360 - A) = Cos A, and Tan(360 - A) = -Tan A.

  • Pythagorean Identity: In a right-angled triangle with hypotenuse r, opposite side y and adjacent side x, we can express the inter-relationships of Sin, Cos and Tan in terms of x, y, and r using the Pythagoras’ Theorem: Sin^2 A + Cos^2 A = 1.

  • Inverse functions: The inverse functions, Sin^-1(x), Cos^-1(x) and Tan^-1(x), give the angle that has x as its Sin, Cos and Tan respectively. Their ranges are -90° to 90° for Sin^-1, 0° to 180° for Cos^-1, and -90° to 90° for Tan^-1.

  • Real world applications: Trigonometry is not just about solving problems in textbooks. It can be applied in real life such as in architecture, navigation, sound wave analysis etc. Hence, practising a variety of problems helps build familiarity and skills.