SOLUTION: If cos(t)=-5/6 where pi < t < 3pi/2 , find the values of the following trigonometric functions. Note: Give exact answers, do not use decimal numbers. The answer should be a fra

Question 1102370: If cos(t)=-5/6 where pi < t < 3pi/2 , find the values of the following trigonometric functions.

Note: Give exact answers, do not use decimal numbers. The answer should be a fraction or an arithmetic expression. If the answer involves a square root it should be enter as sqrt; e.g. the square root of 2 should be written as sqrt(2).
cos(2t) =
sin(2t)=
cos(t/2)=
sin(t/2)=
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Look up "Half angle formulas" on Wikipedia.

Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
.
If cos(t)=-5/6 where pi < t < 3pi/2 , find the values of the following trigonometric functions.

cos(2t) =
sin(2t)=
cos(t/2)=
sin(t/2)=
~~~~~~~~~~~~~~~~

You are given that cos(t) = and the angle "t" is in QIII. Then sin(t) = = = = = . Notice that I put the sign "-" (minus) at sqrt, since the function sine is NEGATIVE in QIII. The next steps are straightforward. a) cos(2t) = cos^2(t) - sin^2(t) = = = = . b) sin(2t) = 2*sin(t)*cos(t) = = . c) cos(t/2) = = = = = = = . Again, the sign is "-" at sqrt, since cosine is NEGATIVE function in QII, where the angle t/2 is. d) sin(t/2) = = = = = = = . The sign is "+" at sqrt, since the sine function is POSITIVE in QII, where the angle t/2 is.

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There are two useful groups of lessons in this site, relevant to this problem.

First group is the lesson
    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS
and all associated lessons (links) with it.

The second group is these lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
    - Evaluating trigonometric expressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the parts of this online textbook under the topics
"Trigonometry. Formulas for trigonometric functions"   and   "Trigonometry: Solved problems".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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