SOLUTION: Let t be a real number with cos(t)=3/7, 3pi/2<t<2pi Find the exact value for each of the following: a. sin(t+3pi/2) b. sec(-t) c. cos(2pi) d.cos(4pi/3 - t) Please

Algebra ->  Trigonometry-basics -> SOLUTION: Let t be a real number with cos(t)=3/7, 3pi/2<t<2pi Find the exact value for each of the following: a. sin(t+3pi/2) b. sec(-t) c. cos(2pi) d.cos(4pi/3 - t) Please      Log On


   

Question 960729: Let t be a real number with cos(t)=3/7, 3pi/2 Find the exact value for each of the following:
a. sin(t+3pi/2)
b. sec(-t)
c. cos(2pi)
d.cos(4pi/3 - t)
Please explain what these means how these are solved I have to understand!
Thank you! in advance
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let t be a real number with cos(t)=3/7, 3pi/2 Find the exact value for each of the following:
Note:: If cos(t) = 3/7, sin(t) = sqrt[7^2-3^2]/7 = 2sqrt(10)/7
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a. sin(t+3pi/2) -sin(t) = -3/7
Use the formula for sin(a+b) = sin(a)cos(b)+cos(a)sin(b)
= (2sqrt(10)/7)(0)+(3/7)(-1) = -3/7
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b. sec(-t) = 1/cos(-t) = 1/cos(t) = 7/3
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c. cos(2pi) = cos(0) = 1
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d.cos(4pi/3 - t) = cos(4pi/3)*cos(t)+sin(4pi/3)*sin(t)
= (-cos(pi/3)*(3/7)+(-sin(pi/3)(2sqrt(10)/7)
= (-1/2)(3/7)+(-sqrt(3)/2)(2sqrt(10)/7)
= (-3/14)-2sqrt(30)/14
= -(3+2sqrt(30))/14
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Cheers,
Stan H.
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Please explain what these means how these are solved I have to understand!