Find the exact value of the expression without a calculator:
sin(3π/4+5π/6)
I've done:
sin(9π/12 + 10π/12)
=sin(19π/12)
What do I do now? Im confused if that would just be the answer or what? Wouldnt the answer be numerical?
sin(19π/12) = sin(3π/2 + π/12) = -cos(π/12)
Now use the half-angle formula to evaluate that.
Thank you!
tan(-15)
To find the exact value of the expression sin(3π/4 + 5π/6), we can simplify it further.
We have already simplified it to sin(19π/12), which is a non-standard angle. To find the exact value, we need to find an angle between 0 and 2π (or 0 and 360 degrees) that is equivalent to 19π/12.
One way to do this is to convert 19π/12 into degrees. Recall that 2π radians is equal to 360 degrees.
We can set up the following proportion:
(19π/12) radians = x degrees
2π radians = 360 degrees
Cross-multiplying, we have:
(19π/12) * 360 = 2π * x
Simplifying:
(19 * 360)π/12 = 2π * x
Cancelling out the π and dividing by 2, we have:
(19 * 360)/12 = x
Calculating, we get:
x = 57π/6 = 570/6 = 95 degrees
So, sin(3π/4 + 5π/6) is equivalent to sin(95 degrees).
Now, we can find the exact value of sin(95 degrees) using a trigonometric identity or a unit circle.
Using the unit circle, we find that sin(95 degrees) = sin(180 degrees - 95 degrees) = sin(85 degrees).
Therefore, the exact value of sin(3π/4 + 5π/6) is sin(85 degrees).