find the 6 trigonometric functions of tan (-3/8): sin < Ø
If you want good answers, post good questions. If you meant
find the 6 trigonometric functions of θ, where tanθ = -3/8 and θ < π
then, knowing that the hypotenuse is √(3^2+8^2) = √73,
sinθ = 8/√73
cosθ = -3/√73
. . .
To find the six trigonometric functions of tan (-3/8), we can use the relationship between tangent, sine, and cosine. Before we do that, we need to find the angle Ø associated with the tangent value.
To find Ø, we can use the inverse tangent function also known as arctan or tan^(-1). We have:
Ø = arctan(-3/8)
Using a calculator or online trigonometric calculator, enter -3/8 and find the arctan or tan^(-1) function to get the angle Ø. Let's assume Ø is -0.367.
Once we have the angle Ø, we can find the sine (sin Ø), cosine (cos Ø), tangent (tan Ø), cosecant (csc Ø), secant (sec Ø), and cotangent (cot Ø) of this angle.
1. Sine (sin Ø):
sin Ø = sin(-0.367)
Note: Since sine is an odd function, sin(-x) = -sin(x).
2. Cosine (cos Ø):
cos Ø = cos(-0.367)
Note: Since cosine is an even function, cos(-x) = cos(x).
3. Tangent (tan Ø):
tan Ø = tan(-0.367)
4. Cosecant (csc Ø):
csc Ø = 1/sin Ø
5. Secant (sec Ø):
sec Ø = 1/cos Ø
6. Cotangent (cot Ø):
cot Ø = 1/tan Ø
Using a scientific calculator or a trigonometric table, plug in the value of Ø (-0.367) into the sine, cosine, tangent, cosecant, secant, and cotangent functions to find their respective values.
Remember to use parentheses when entering the angle in trigonometric functions to ensure correct calculations.