SOLUTION: given that sin(theta) equals (1/5)and that the terminal side is in quadrant I, find exact answers for cos(theta+(pi/4))
Algebra ->
Trigonometry-basics
-> SOLUTION: given that sin(theta) equals (1/5)and that the terminal side is in quadrant I, find exact answers for cos(theta+(pi/4))
Log On
Question 851224: given that sin(theta) equals (1/5)and that the terminal side is in quadrant I, find exact answers for cos(theta+(pi/4)) Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! given that sin(theta) equals (1/5)and that the terminal side is in quadrant I, find exact answers for cos(theta+(pi/4))
----
If sin(t) = 1/5, cos(t) = sqrt(5^2-1^2)/5 = 2sqrt(6)/5
-----------------
Then cos(t+(pi/4)] = cos(t)*cos(pi/4)-sin(t)sin(pi/4)
=======
= (sqrt(2)/2)(cos(t)+sin(t))
=======
= (sqrt(2))/2)((1/5)+(2sqrt(6)/5]
-------
= (sqrt(2)/2)(1+2sqrt(6))/5
----
= (sqrt(2)+4sqrt(3))/10
===========================
Cheers,
Stan H.
==========
(