Question 789386: I have 2 questions"
1)Find all values of θ that satisfy the equation over the interval [0, 2π].
cos theta = sin theta. Please help me solve this problem. I do not know where to begin. I looked through some notes and tried a few answers and they are not coming out correct. The question asks that I give the smaller and larger values in rad.
2)And the second is given cos theta= 7/8. Find the other 5 trig functions of theta. I found sec theta as 8/7. but how would I use those 2 to find the other 4 functions?
Thank you for your help,
Jolene
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! note that pi in trig equals 180 degrees so problem 1 is asking for all values from 0 to 360 degrees where cos theta = sin theta which covers all four quadrants
1) here we go :-)
cos theta = sin theta implies cos theta equals cos (pi/2 - theta), this implies that theta = 2n*pi + (pi/2 - theta) where n is 0, 1, 2, 3, 4, ....., so 2*theta = 2n*pi +pi/2 implies theta = n*pi + pi/4 , which satisfies the relation
we see that cos theta = sin theta for theta = 45 or 225 degrees
now convert these angles to radians by multiplying degrees by pi/180
therefore we have pi/4 and 5*pi/4
2)we are given cos theta = 7/8
using the relation a^2 + b^2 = c^2 we get
a^2 + 7^2 = 8^2
a^2 = 64 -49 = 15
a = 3.8
from this we have
sin = 3.8 / 8
cos = 7 / 8
tan = 3.8 / 7
csc = 8 / 3.8
sec = 8 / 7
cot = 7 / 3.8
|
|
|
