SOLUTION: For the acute angle θ , where sinθ=1/√2 , find (cos(π+θ)) and (sec(π/2)+θ))
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Question 826573: For the acute angle θ , where sinθ=1/√2 , find (cos(π+θ)) and (sec(π/2)+θ))
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
We've been given that . Let's see what happens if we rationalize the denominator:
We should now recognize (if we had not already) that this sin value is a special angle value for sin. is a special angle. Specifically it is .
Now that we know we can solve our problems.
is an angle which terminates in the 3rd quadrant. The reference angle is and cos is negative in the 3rd quadrant. Since
For this one we cannot just see the reference angle like we did before. So we will add the fractions and see where are are:
is an angle which terminates in the second quadrant (since it is more than but less than . The reference angle will be . Since sec is the reciprocal of cos, it will have the same sign. cos is negative in the second quadrant so sec will be negative, too. And since :
Rationalizing the denominator:
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