SOLUTION: Write the exact value of sin(3π/4)

Algebra ->  Trigonometry-basics -> SOLUTION: Write the exact value of sin(3π/4)      Log On


   

Question 1204874: Write the exact value of
sin(3π/4)
Found 3 solutions by ikleyn, mccravyedwin, math_tutor2020:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is the Table angle.


sin%283pi%29%2F4 = sqrt%282%29%2F2.


Each student must know Trigonometry functions values of Table angles, 
as he/she knows  multiplication table.

Solved.

Happy learning.


Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!

Maybe this might help for the 1st quadrant.  Notice how the
sines and cosines are all written in the form sqrt%28N%29%2F2 
rather than all simplified, so you can see a pattern.



Here it is like that for all the basic 3 trig values sine, cosine, and tangent.
 
 

Edwin

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: sqrt%282%29%2F2


Explanation

matrix%281%2C5%2C%283pi%29%2F4%2C%22radians%22%2C%22=%22%2C135%2C%22degrees%22%29 because of this scratch work: %28%283pi%29%2F4%29%2A%28180%2Fpi%29+=+135

The angle 135 degrees is in quadrant 2 (northwest quadrant) where 90 < theta < 180.

The reference angle for this quadrant is 180-theta = 180-135 = 45

Then, sin%2845%5Eo%29+=+sqrt%282%29%2F2 which is something you should memorize.
Recall that sine is positive in Q2.

Therefore, sin%28%283pi%29%2F4%29+=+sqrt%282%29%2F2

--------------------

A shortcut is to use the unit circle to locate angle 3pi%2F4 radians in the upper left quadrant.

Image Source:
https://www.mathsisfun.com/geometry/unit-circle.html
You have to scroll down quite a bit to reach this diagram.

This angle has the terminal point where its y coordinate is y+=+sqrt%282%29%2F2, which is the sine of the angle mentioned.

This is another way to see how sin%28%283pi%29%2F4%29+=+sqrt%282%29%2F2

Side notes:
You don't have to memorize the entire unit circle.
Memorize only Q1 and then use symmetry to fill out the rest (or fill out what you need).
However, if the teacher is reasonable and generous, then s/he should allow the unit circle as a reference sheet on exams.
In real world settings, people use reference sheets and books all the time. Why else would people write them?