https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/v/trigonometric-ratios-for-common-angles 2025-03-01T15:52:37.13987578Z Trigonometric ratios for common angles In this video, we look at the trigonometric rations (sin, cos, and tan) for some common angles. We first define the trigonometric ratios as the coordinates of points on the unit circle. First we look at the multiples of pi/2. We then use geometry (right angled triangles and equilateral triangles) to find the coordinates for some other common angles - pi/4, pi/3, and pi/6. Finally, we generate the table for sin, cos, and tan for these angles. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Trigonometric ratios for common angles In this video, we look at the trigonometric rations (sin, cos, and tan) for some common angles. We first define the trigonometric ratios as the coordinates of points on the unit circle. First we look at the multiples of pi/2. We then use geometry (right angled triangles and equilateral triangles) to find the coordinates for some other common angles - pi/4, pi/3, and pi/6. Finally, we generate the table for sin, cos, and tan for these angles. https://cdn.kastatic.org/ka-youtube-converted/nUMtbVtnN-E.mp4/nUMtbVtnN-E.mp4 610 The unit circle https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/v/sign-of-trigonometric-functions 2025-03-01T15:52:37.13987578Z Sign of trigonometric functions In this video, we learn how to figure out the signs of trigonometric functions using the unit circle. We first figure out where cos, sin, and tan are positive and negative using the coordinates of the points representing the angles. We then practice this skill by solving some problems. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Sign of trigonometric functions In this video, we learn how to figure out the signs of trigonometric functions using the unit circle. We first figure out where cos, sin, and tan are positive and negative using the coordinates of the points representing the angles. We then practice this skill by solving some problems. https://cdn.kastatic.org/ka-youtube-converted/wk-YlhE5c7Q.mp4/wk-YlhE5c7Q.mp4 409 The unit circle https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/v/using-the-unit-circle-to-find-ratios-of-common-angles 2025-03-01T15:52:37.13987578Z Using the unit circle to find ratios of common angles We've learnt how to find the trigonometric ratios for some common angles like pi/3, pi/4, and pi/6. In this video, we'll move beyond the first quadrant to get 9 more points on the unit circle. Using symmetry, we'll find the coordinates of these points which will help us figure out the cos and sin of these angles. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Using the unit circle to find ratios of common angles We've learnt how to find the trigonometric ratios for some common angles like pi/3, pi/4, and pi/6. In this video, we'll move beyond the first quadrant to get 9 more points on the unit circle. Using symmetry, we'll find the coordinates of these points which will help us figure out the cos and sin of these angles. https://cdn.kastatic.org/ka-youtube-converted/CKYG2EgeeYk.mp4/CKYG2EgeeYk.mp4 397 The unit circle https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/v/adding-subtracting-from-multiples-of-pi-2 2025-03-01T15:52:37.13987578Z Adding subtracting from multiples of pi/2 We've learnt how to find trigonometric ratios for some common angles across all quadrants. We expand on this concept by generalising the learnings and applying them on a random point in the first quadrant. We first look at adding and subtracting from multiples of pi and then observe what happens if we do the same for multiples of pi/2. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Adding subtracting from multiples of pi/2 We've learnt how to find trigonometric ratios for some common angles across all quadrants. We expand on this concept by generalising the learnings and applying them on a random point in the first quadrant. We first look at adding and subtracting from multiples of pi and then observe what happens if we do the same for multiples of pi/2. https://cdn.kastatic.org/ka-youtube-converted/e1dGuOcjGuM.mp4/e1dGuOcjGuM.mp4 550 The unit circle https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/v/finding-other-five-ratios 2025-03-01T15:52:37.13987578Z Finding other five ratios In this video, we'll learn how to find the remaining trigonometric ratios when one of them is given along with some information on where the angle is (in which quadrant). We first analyse the triangle that the angle is forming, then place it on the unit circle, and finally, after figuring out exactly where the angle is on the circle, we use the coordinates of the corresponding point on the circle to get the remaining ratios. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Finding other five ratios In this video, we'll learn how to find the remaining trigonometric ratios when one of them is given along with some information on where the angle is (in which quadrant). We first analyse the triangle that the angle is forming, then place it on the unit circle, and finally, after figuring out exactly where the angle is on the circle, we use the coordinates of the corresponding point on the circle to get the remaining ratios. https://cdn.kastatic.org/ka-youtube-converted/OnG9g0qM_A8.mp4/OnG9g0qM_A8.mp4 423 The unit circle https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/v/using-the-unit-circle-to-find-tan-17pi-6 2025-03-01T15:52:37.13987578Z Using the unit circle to find tan(17pi/6) In this video, we solve some problems where we find values of trigonometric functions for given angles using the unit circle. We first find sin(765 degrees), then tan(19pi/3) and finally look at tan(17pi/6). For the last problem, we try three different methods. We solve it using multiples of pi, pi/2, and also plugging values in the formulae. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Using the unit circle to find tan(17pi/6) In this video, we solve some problems where we find values of trigonometric functions for given angles using the unit circle. We first find sin(765 degrees), then tan(19pi/3) and finally look at tan(17pi/6). For the last problem, we try three different methods. We solve it using multiples of pi, pi/2, and also plugging values in the formulae. https://cdn.kastatic.org/ka-youtube-converted/x81og-c095s.mp4/x81og-c095s.mp4 426 The unit circle https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:unit-circle/v/unit-circle-definition-of-trig-functions-1 2021-06-30T17:32:39Z Unit circle Learn how to use the unit circle to define sine, cosine, and tangent for all real numbers. Sal Khan video https://cdn.kastatic.org/googleusercontent/4va3CHgzmCX8w1NMhs0LlyYxLMiXHDwZ-dDm8quQ0X5OKdz1Yj1KGmmUatzGzQcx5s4jzRHet0bYdh0NK-KNxB3iTw Unit circle Learn how to use the unit circle to define sine, cosine, and tangent for all real numbers. https://cdn.kastatic.org/ka-youtube-converted/1m9p9iubMLU.mp4/1m9p9iubMLU.mp4 544 The unit circle https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/e/plotting-angles-on-unit-circle 2026-04-07T22:59:30.107127435Z Plotting angles on unit circle For given angle, find its position on the unit circle. exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:radians/e/unit-circle-with-radians 2025-03-01T15:52:37.13987578Z Unit circle (with radians) Get more practice with the unit circle definition of sine and cosine, this time with radians instead of degrees. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:unit-circle/v/matching-ratios-trig-functions 2021-06-30T17:32:35Z The trig functions & right triangle trig ratios Sal shows how, for acute angles, the two different definitions of the trigonometric values (SOH CAH TOA and the unit circle definition) result in the same values. Sal Khan video https://cdn.kastatic.org/googleusercontent/c0UdQAIw0Z9Y4urOKTHbmOHKFTJHkq7hOgH3dDSYlUf2TnGutCehCIcgi4p5iBxnlOEdinR2IhzIwUgqGyl3NnBy The trig functions & right triangle trig ratios Sal shows how, for acute angles, the two different definitions of the trigonometric values (SOH CAH TOA and the unit circle definition) result in the same values. https://cdn.kastatic.org/ka-youtube-converted/WffVdYETdng.mp4/WffVdYETdng.mp4 417 The unit circle https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:special-angles/v/solving-triangle-unit-circle 2021-06-30T17:32:34Z Trig values of π/4 Sal finds the trigonometric values of π/4 using the unit-circle definition. Sal Khan video https://cdn.kastatic.org/googleusercontent/KR3yVel6ABULTaZmJ3T74ecv_lm4WfLV40v28QuXhprHX--TwL20KNi2dDhmMqdpBDQSOSUYfmOrcu8AasFsTJKmpg Trig values of π/4 Sal finds the trigonometric values of π/4 using the unit-circle definition. https://cdn.kastatic.org/ka-youtube-converted/KoYZErFpZ5Q.mp4/KoYZErFpZ5Q.mp4 474 The unit circle https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb89:special-angles/e/trigonometric-functions-of-special-angles 2025-03-01T15:52:37.13987578Z Trig values of special angles Find the sine and cosine of special angles, which are angles whose trig values we can determine without the use of a calculator. Sulinya Ramanan exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/e/sign-of-trigonometric-functions 2026-04-07T22:59:30.107127435Z Sign of trigonometric functions Find sign of sin, cos and tan for given angle or given quadrant. exercise https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:trigonometric-functions-ncert-new/x0419e5b3b578592a:the-unit-circle/e/find-value-of-other-trigonometric-functions-from-given-trigonometric-function 2025-03-01T15:52:37.13987578Z Find value of other trigonometric functions from given trigonometric function Similar to NCERT problems. One function and quadrant of angle is given. Find another function value. exercise