If Sin Teta =3/5.Find Tan Teta For Teta Degree <teta<90degree
3,4,5 right triangle
sin T = 3/5
cos T = 4/5
tan T = 3/4
To find the value of Tan Teta given that Sin Teta is equal to 3/5, we can use the following trigonometric identity:
Tan Teta = Sin Teta / Cos Teta
First, we need to find the value of Cos Teta. We know that Sin Teta is equal to 3/5, and we can use the Pythagorean identity to solve for Cos Teta. The Pythagorean identity states:
Sin^2 Teta + Cos^2 Teta = 1
Rearranging the equation, we have:
Cos^2 Teta = 1 - Sin^2 Teta
Cos^2 Teta = 1 - (3/5)^2
Cos^2 Teta = 1 - 9/25
Cos^2 Teta = 16/25
Taking the square root of both sides, we get:
Cos Teta = ± √(16/25)
Cos Teta = ± (4/5)
Since Teta is between 0 and 90 degrees, the value of Cos Teta should be positive. Thus, we have:
Cos Teta = 4/5
Now, we can substitute the values of Sin Teta and Cos Teta into the Tan Teta formula:
Tan Teta = Sin Teta / Cos Teta
Tan Teta = (3/5) / (4/5)
Tan Teta = (3/5) * (5/4)
Tan Teta = 3/4
Therefore, the value of Tan Teta given that Sin Teta is equal to 3/5 is 3/4.