SOLUTION: Find the exact values of sin 2θ, cos 2θ, and tan 2θ for the given value of θ. cos θ = 3/5; 0° < θ < 90° a).sin 2θ b).cos 2θ c).tan 2θ Please help! I want to

Question 1158677: Find the exact values of sin 2θ, cos 2θ, and tan 2θ for the given value of θ.
cos θ = 3/5; 0° < θ < 90°
a).sin 2θ
b).cos 2θ
c).tan 2θ
Please help! I want to know how to solve these kind of problems so please don't just show me the answer. Thank you :)
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If you google "double angle formulas", you can find
the cos, sin, and tan of
------------------------------------------
You are given that
and
This means the angle is in the 1st quadrant where the
cos, sin, and tan are all positive (+) / (+)
--------------------------------------------
(a)
( look it up online )
Note that if , you have a 3-4-5 triangle, so
and

( all positive in the 1st quadrant )

-----------------------------------
(b)
( online )

The negative sign tells me that ends up in the
2nd quadrant where the cosine is negative.
-------------------------------
(c)
( online )

It's negative because the tan is negative in the 2nd quadrant
Notice also that:

Also notice that I never had to find out what was to
solve these. But from the results, I know that MUST be
greater than 45 degrees, in order for to end up
in the 2nd quadrant. I'll show this using my calculator:

degrees
and which is in the 2nd quadrant
-------------------------------
Hope all this helps

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