159k views
2 votes
If tant = 5 12 and T < t< 2 31 find sint, cost, sect, csct,

cott. Enter the exact answers

1 Answer

4 votes

To find the values of the trigonometric functions, we need to determine the ratios for the given tangent value (tan(t)) and restrict the angle t to the given interval (T < t < 2π/31).

Given: tan(t) = 5/12

From this, we can determine the values of the other trigonometric functions:

sin(t) = (5/12) / sqrt(1 + (5/12)^2)

cos(t) = 1 / sqrt(1 + (5/12)^2)

sec(t) = 1 / cos(t)

csc(t) = 1 / sin(t)

cot(t) = 1 / tan(t)

Let's calculate these values:

sin(t) = (5/12) / sqrt(1 + (5/12)^2) = (5/12) / sqrt(1 + 25/144) = (5/12) / sqrt(169/144) = (5/12) / (13/12) = 5/13

cos(t) = 1 / sqrt(1 + (5/12)^2) = 1 / sqrt(1 + 25/144) = 1 / sqrt(169/144) = 1 / (13/12) = 12/13

sec(t) = 1 / cos(t) = 1 / (12/13) = 13/12

csc(t) = 1 / sin(t) = 1 / (5/13) = 13/5

cot(t) = 1 / tan(t) = 1 / (5/12) = 12/5

Therefore, the exact values of the trigonometric functions within the given interval are:

sin(t) = 5/13

cos(t) = 12/13

sec(t) = 13/12

csc(t) = 13/5

cot(t) = 12/5

User Toney
by
7.7k points

Related questions

asked Aug 3, 2024 154k views
Liu Peng asked Aug 3, 2024
by Liu Peng
7.8k points
1 answer
2 votes
154k views
asked Jan 14, 2024 2.0k views
Ericslaw asked Jan 14, 2024
by Ericslaw
7.8k points
1 answer
0 votes
2.0k views
asked Mar 26, 2024 118k views
Javi asked Mar 26, 2024
by Javi
7.9k points
1 answer
3 votes
118k views