Question

Find the exact values of the sine, cosine, and tangent of the angle.

11π/12 = 3π/4 + π/6.
how will I determine
Sin 11π/12, Cos 11π/12, and Tan 11π/12?

Answer 1

To find the exact values of sin(11π/12), cos(11π/12), and tan(11π/12), we can use the sum of angle formulas for trigonometric functions.

Step-by-step explanation:

To find the exact values of the sine, cosine, and tangent of the angle 11π/12, we need to use the trigonometric identities. From the given equation, 11π/12 = 3π/4 + π/6, we can see that the angle 11π/12 is the sum of 3π/4 and π/6. Therefore, we can use the sum of angle formulas to find the sine, cosine, and tangent.

Using the formula sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we can find that sin(11π/12) = sin(3π/4 + π/6) = sin(3π/4)cos(π/6) + cos(3π/4)sin(π/6).

Similarly, we can use the formula cos(a + b) = cos(a)cos(b) - sin(a)sin(b) to find cos(11π/12) and the formula tan(a + b) = (tan(a) + tan(b))/(1 - tan(a)tan(b)) to find tan(11π/12).