SOLUTION: Can you solve for theta if cos0= negative square root of 2 by 2. Also, i am limited to the third and fourth quadrant. I figured the answer had to be either 7pi by 6 or 5 pi by 4. M

Question 1006799: Can you solve for theta if cos0= negative square root of 2 by 2. Also, i am limited to the third and fourth quadrant. I figured the answer had to be either 7pi by 6 or 5 pi by 4. My book said 5 pi by 4 but how would I know which special triangle to use?
Answer by HaundC(1) (Show Source): You can put this solution on YOUR website!
For that case, theta WOULD be 5pi/4.
For 30 degree triangles (pi/6, 5pi/6, 7pi/6, 11pi/6), your sine will always be +/-(sqrt(3))/2, your cos will always be +/-1/2, and your tan will always be +/-(sqrt(3))/3.
For a 45 degree triangle (pi/4, 3pi/4, 5pi/4, 7pi/4), your sin and cos will always be +/-(sqrt(2))/2, and your tan will always be +/-1.
For a 60 degree triangle (pi/3, 2pi/3, 4pi/3, 5pi/3), your sin will always be +/-(sqrt(3)/2, your cos will always be +/-1/2, and your tan will always be (sqrt(3)).
(whether they are positive or negative depend on what quadrant they are in)
It's a matter of just memorizing.
RELATED QUESTIONS
Suppose cosine of theta equals the negative square root of 3 over or divided by 4 and... (answered by lwsshak3)

Alright, I don't understand any of this, and I'm a mathematical genius. If you could... (answered by Alan3354)

I need to find the value of tan(theta) but the only value I have is sin(theta)=1/4 and it (answered by jim_thompson5910)

Given sec t = -4 and t is in quadrant 3, find the other 5 trig functions of t. At... (answered by lwsshak3)

if tangent theta = square root of 2 over 4 and angle theta terminates in the first... (answered by stanbon)

How do you find csc theta in terms of cos theta if theta is in quadrant four ? I have... (answered by Alan3354)

Are each of the statements below true or false? Explain you answer. Part 1 sq rt (a) +... (answered by Fombitz)

The question is : For i = the square root of -1, if 3i (2 + 5i) = x + 6i, then x = ?... (answered by richard1234)

If sin theta= 2/3 and theta is in Quadrant I, what is the value of (tan theta)(cos... (answered by stanbon)