guglchristian.blogg.se - All students take calculus

If you remember those set of numbers, you can work out sin and cos of any common value anywhere on the unit circle. 0014Īnd then there is the 30, 60, 90 triangle whose values are 1/2, (root 3)/2 and 1. There is the 45, 45, 90 triangle whose values are (root2)/2, (root 2)/2 and 1. Remember what we learned, everything comes back to knowing those two key triangles. Hi we are working out some examples of common values of sin and cos of common angles. Since is in quadrant II we know that sine will be positive and cosine will be negative.Note that 150 ° is 30 ° from the x - axis so we can use the 30 ° - 60 ° - 90 ° triangle to find the sine and cosine.This will help us to solve for the sine and cosine values as well. Looking at our picture, we see that is in quadrant II.First convert 150 ° to radians by using the following formula: degree measure × = radian measure.Since 135 ° is in quadrant II we know that sine will be positive and cosine will be negativeĬonvert 150 ° to radians, identify its quadrant, and find its cosine and sine.Recall that cosine is the x coordinate and sine is the y coordinate of 135 ° on the unit circle.Note that is from the x - axis so we can use the 45 ° − 45 ° − 90° triangle to find the sine and cosine.Looking at our picture, we see that 135 ° is in quadrant II.This will help you to determine the quadrant it is in and it will also help you to find the sine and cosine values. Locate 135 ° on a unit circle (draw a picture).Since is in quadrant III we know that tangent will be positive so cosine and sine will be negative.Note that 210 ° is 30 ° past the x - axis so we can use the 30 ° − 60 ° − 90 ° triangle to find the sine and cosine.Looking at our picture, we see that is in quadrant III.

First convert 210 ° to radians by using the following formula: degree measure × = radian measure.Since 240 ° is in quadrant III we know that tangent will be positive so sine and cosine will be negativeĬonvert 210 ° to radians, identify its quadrant, and find its cosine and sine.

Recall that cosine is the x coordinate and sine is the y coordinate of 240 ° on the unit circle.

Note that is past the x - axis so we can use the 30 ° − 60 ° − 90 ° triangle to find the sine and cosine.

Looking at our picture, we see that 240 ° is in quadrant III.

Locate 240 ° on a unit circle (draw a picture).

First convert to degrees by using the following formula: radian measure × = degree measure.

Since is in quadrant IV we know that cosine will be positive and sine will be negativeĬonvert to degrees, identify its quadrant, and find its cosine and sine.

Using the Mnemonic ASTC (All Students Take Calculus) helps to determine which values are positive in which quadrant.

Recall that cosine is the x coordinate and sine is the y coordinate of on the unit circle.

Note that 315 ° is 45 ° from the x - axis so we can use the 45 ° − 45 ° − 90 ° triangle to find the sine and cosine.

Looking at our picture, we see that is in quadrant IV.

Locate on a unit circle (draw a picture).

First convert 315 ° to radians by using the following formula: degree measure × = radian measure.

Convert 315 ° to radians, identify its quadrant, and find its cosine and sine.