SOLUTION: I need help finding the value of the trig functions 1. Use special right triangles to state the value of the 6 trig functions for 30 degrees, 45 degrees and 60 degrees

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Question 1137376: I need help finding the value of the trig functions
1. Use special right triangles to state the value of the 6 trig functions for 30 degrees, 45 degrees and 60 degrees
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


As you begin studying trigonometry, you need to be able to quickly find the values of the trig functions for these special angles. Rote memorization is not a particularly good method; having a picture in your mind of where those angles comes from is a much more reliable method.

For the 45 degree angle, think of the diagonal of a square. If the side lengths of the square are 1, then the diagonal (by the Pythagorean Theorem) is sqrt(2). Then

sin(45) = cos(45) = 1%2Fsqrt%282%29+=+sqrt%282%29%2F2
tan(45) = sin%2845%29%2Fcos%2845%29+=+1
cot(45) = 1%2Ftan%2845%29+=+1%2F1+=+1
sec(45) = 1%2Fcos%2845%29+=+sqrt%282%29
csc(45) = 1%2Fsin%2845%29+=+sqrt%282%29

For the 30 and 60 degree angles, think of an equilateral triangle cut in half; that forms two 30-60-90 right triangles. If the side length of the triangle is 1, then the short side of each 30-60-90 right triangle is 1/2 (half the length of a side of the triangle). Then the Pythagorean Theorem give us the length of the long leg of each 30-60-90 right triangle as sqrt(3)/2. Then

sin(30) = cos(60) = %281%2F2%29%2F1+=+1%2F2
cos(30) = sin(60) = %28sqrt%283%29%2F2%29%2F1+=+sqrt%283%29%2F2
tan(30) = cot(60) = %281%2F2%29%2F%28sqrt%283%29%2F2%29+=+1%2Fsqrt%283%29+=+sqrt%283%29%2F3
csc(30) = sec(60) = 1%2F%281%2F2%29+=+2
csc(60) = sec(30) = 1%2F%28sqrt%283%29%2F2%29+=+2%2Fsqrt%283%29
cot(30) = tan(60) = 1%2F%281%2Fsqrt%283%29%29+=+sqrt%283%29