Question

Найдите cos a, tg a, ctg a, если : sin a=1/2; sin a = 40/41; sin a= 0,5

Answer 1

1. cos=+- √3/2 tg= +- 1/√3 ctg=+-√3
2. cos= √(1-sin^2) = =9/41 tg=40/9 ctg=9/40
3. 1/2=0.5 посмотри на 1 пункт

Answer 2

To find the values of cosine (cos a), tangent (tg a), and cotangent (ctg a) for the given values of sine (sin a), we can use the Pythagorean identity and the definitions of tangent and cotangent. Let's calculate each case:

1. sin a = 1/2 We know that sin a = 1/2, and we can use the Pythagorean identity to find cos a:

cos^2 a + sin^2 a = 1 cos^2 a + (1/2)^2 = 1 cos^2 a + 1/4 = 1 cos^2 a = 1 - 1/4 cos^2 a = 3/4

Since cos a is positive (because the sine is positive), we take the positive square root:

cos a = √(3/4) = √3/2

Now, we can find the tangent and cotangent using their definitions:

tg a = sin a / cos a tg a = (1/2) / (√3/2) tg a = 1 / √3 = √3 / 3

ctg a = cos a / sin a ctg a = (√3/2) / (1/2) ctg a = √3

2. sin a = 40/41 For this case, we'll use the same approach:

cos^2 a + sin^2 a = 1 cos^2 a + (40/41)^2 = 1 cos^2 a + 1600/1681 = 1 cos^2 a = 1 - 1600/1681 cos^2 a = 81/1681

Again, we take the positive square root since cos a is positive:

cos a = √(81/1681) = 9/41

Now, we find the tangent and cotangent:

tg a = sin a / cos a tg a = (40/41) / (9/41) tg a = 40/9

ctg a = cos a / sin a ctg a = (9/41) / (40/41) ctg a = 9/40

3. sin a = 0.5 Using the same approach:

cos^2 a + sin^2 a = 1 cos^2 a + (0.5)^2 = 1 cos^2 a + 0.25 = 1 cos^2 a = 1 - 0.25 cos^2 a = 0.75

Again, taking the positive square root:

cos a = √(0.75) = √3/2

Now, let's find the tangent and cotangent:

tg a = sin a / cos a tg a = 0.5 / (√3/2) tg a = 1 / √3 = √3 / 3

ctg a = cos a / sin a ctg a = (√3/2) / 0.5 ctg a = √3

To summarize:

1. For sin a = 1/2: cos a = √3/2 tg a = √3 / 3 ctg a = √3

2. For sin a = 40/41: cos a = 9/41 tg a = 40/9 ctg a = 9/40

3. For sin a = 0.5: cos a = √3/2 tg a = √3 / 3 ctg a = √3

Please note that the values of cos a and ctg a are the same for cases 1 and 3 because the sine values are the same.