If you want to convert radians to degrees, simply multiply the number of radians by 180/?.Ī reference angle is always positive and is ? 90º. If you want to convert degrees into radians, simply multiply the number of degrees by. In the fourth quadrant, only Cosine is positiveĭid this help? Learn more topics in Trigonometry and 100 other subjects at, the best place to get in-depth and instant homework help online. In the third quadrant, only Tangent is positive.In the second quadrant, only Sine is positive.In the first quadrant, All are positive.The mnemonic ASTC (All Students Take Calculus) can help you remember which ones (sine, cosine, tangent) are positive in which quadrant. You can find the values for 60° angle the same way. If you have trouble with this concept, please check out our in-depth SohCahToa guide. Now you can find the sine, cosine and tangent using soh cah toa. According to Pythagorean theorem, the new side is ?3. (All sides are 2 and all angles are 60°.)Ĭut it in half. Sketch an equilateral triangle with side length 2. So actually, it’s just these three numbers: that you need to memorize.Īnother way to help you remember the 30° and 60° is the special triangle. The denominator is 2 and will stay the same. The denominator is 2 and will stay the same.įor cosine of 30°, 45°, and 60°, you should try to think “3, 2, 1” for the square root number in the numerator. Remembering the Unit Circleįor sine of 30°, 45°, and 60°, you should try to think “1, 2, 3” for the square root number in the numerator. This might seem a lot at first, but there’s a trick to help you learn this faster. There are some important angles whose sine, cosine and tangent you should memorize. To find the cosine of the same angle, you just look up for the x coordinate of the same point. If you are asked to find sin60°, you would just need to look up for the y coordinate of the intersecting point on the circle. This is called the Pythagorean trigonometric identity and it is very useful. sin ? is the y coordinate of a point where terminal side of the angle intersects the unit circleīut since we have that x = cos ? and y = sin ?, this identity becomes:.cos ? is the x coordinate of a point where terminal side of the angle intersects the unit circle.This formula applies to all the quadrants (it’s not limited to acute angles): This shows us that in a unit circle, cos ? = x and sin ? = y, which creates:Ĭosine is represented by the horizontal leg. Now let’s use some right angle trigonometry. The lengths x and y become the legs of a right triangle whose hypotenuse is actually the radius of our unit circle, i.e. Let (x,y) be the point on the circle that is in the first quadrant. Trigonometry of the Right Triangle and the Unit Circle You don’t have to memorize all the values of the trigonometric functions, you just have to understand the unit circle. For example, it’ll help us find the exact value of sin $latex \frac$ or cos30°. This circle helps us find the exact values of some trigonometric functions and not the decimal approximations the calculator will give us. The unit circle is a circle, centered at the origin, with a radius of 1.
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