Go about it the same way you would if sinΘ were positive, except put the angle in the correct quadrant. Since cosΘ > 0 and sinΘ < 0 , we are in QIV. So draw an acute angle in standard position with its terminal ray in QIV with adjacent leg = 4 and hypotenuse (radius) = 5. This will make the opposite leg = - 3.
Thus, sinΘ = - 3/5 , cosΘ = 4/5 , and tanΘ = -3/4.
Use the double angle formulas to calculate the trig values asked for in the question.
Amber D.
also, I'm given 3 formulas for cos how do I know which one to use???
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04/03/21
Josh F.
tutor
Think of 2 as = 2/1. Remember if you multiply both the numerator and denominator of a fraction by 2 you are not multiplying by anything at all! 2*3 / 2*5 = 6/10 = 3/5.
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04/03/21
Josh F.
tutor
sin(2theta) = 2*sin(theta)*cos(theta)
cos(2theta) = 2cos^2(theta) - 1
tan(2theta) = 2tan(theta)/(1 - tan^2(theta))
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04/03/21
Josh F.
tutor
Whichever's easiest (frequently 2cos^2(theta) - 1, or 1 - 2sin^2(theta), since those only require knowing one of the trig values for theta.
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04/03/21
Amber D.
ok, I'm looking at my professors example questions . it says Sin2Theta = 2 sin theta Cos theta = 2(8/17)(-15/17) .... Sin2Theta = -240/289 . different question but I think I have to follow the same steps to get the answer to my question? I see where she did 8*-15*2 to get -240 and 17*17 to get 289 but why didn't she multiply the bottom numbers (17*17) by 2 like she did the top numbers???04/03/21