Use a cofunction to write an expression equal to csc(4ð/11).
I need help solving this problem. Thank You
What is ð ?
Did you notice that trig co-functions come in pairs:
sine ---cosine
secant --- cosecant
tangent --- cotangent
so csc(4π/11) = ......
To write an expression equal to csc(4π/11) using cofunctions, we can use the reciprocal relationship between sine (sin) and cosecant (csc). The reciprocal of sine is cosecant, so we can express csc(θ) as 1/sin(θ).
Therefore, we can write the expression as:
csc(4π/11) = 1/sin(4π/11)
To find the value of sin(4π/11), we can use a calculator or convert the angle to degrees and use a unit circle. Here, we'll use a calculator:
sin(4π/11) ≈ 0.43388 (rounded to five decimal places)
Now, substituting this back into the expression, we get:
csc(4π/11) ≈ 1/0.43388
To evaluate the expression further, we calculate the reciprocal of 0.43388:
csc(4π/11) ≈ 2.3043 (rounded to four decimal places)
Therefore, an expression equal to csc(4π/11) is approximately 2.3043.