SOLUTION: 2 Theta, given Sin theta=sq rt of 2/3 and cos of theta > 0. Find Cos of theta

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Question 1137903: 2 Theta, given Sin theta=sq rt of 2/3 and cos of theta > 0. Find Cos of theta
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

note:
Quadrant 1: All are positive
Quadrant 2: Sine is positive
Quadrant 3: Tangent is positive
Quadrant 4: Cosine is positive
given:
sin+%28theta%29=sqrt%282%2F3%29+%3E0 ,theta must lie in the 1st or 2nd quadrant
cos%28theta%29+%3E+0.....which it is, theta must lie in the 1st or+4th quadrant

common for both sin+%28theta%29+%3E0 and cos%28theta%29+%3E0 is 1st quadrant
sin+%28theta%29=sqrt%282%2F3%29+=0.816496580927726
theta=sin%5E-1+%280.816496580927726%29
theta=54.7356103172453°
cos%28theta%29+=cos%2854.7356103172453%29=0.577350269189626=>cos%28theta%29%3E0