SOLUTION: Given that cos θ = −16/65, θ in quadrant II, do the following. (a) (4 pts) Draw the triangle for θ. Label. (b) (4 pts each) Find exact values of sin 2θ,

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Question 1064372: Given that cos θ = −16/65, θ in quadrant II, do the following.
(a) (4 pts) Draw the triangle for θ. Label.
(b) (4 pts each) Find exact values of sin 2θ, cos 2θ, and tan 2θ. No decimals.
(c) (2 pts) Determine the quadrant of 2θ. Justify your answer
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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Given that cos θ = −16/65, θ in quadrant II, do the following.
(a) (4 pts) Draw the triangle for θ. Label.
(b) (4 pts each) Find exact values of sin 2θ, cos 2θ, and tan 2θ. No decimals.
(c) (2 pts) Determine the quadrant of 2θ. Justify your answer
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

a)  I will not do a). Instead, YOU do it.


b)   =  =  = . The sign at the square root is "+" since  is positive in Q2.

    ====>   =  =  = calculate.    ( Notice it is negative !)

            =  =  = calculate.     ( Notice it is negative !)


            =  = calculate.

           For it,  and  you just calculated above  (I suppose !).


c)  Since both  and  are negative, the angle  is in Q3.

Completed.


For more solved similar problems on calculating trig functions see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
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 part of this online textbook under the topic "Trigonometry: Solved problems".



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