SOLUTION: if sinx=3/5 and x is an acute angle, use double angle formula to find the exact values of sin2x,cos2x,tan2x and the quadrant of the angle 2x.

Algebra ->  Trigonometry-basics -> SOLUTION: if sinx=3/5 and x is an acute angle, use double angle formula to find the exact values of sin2x,cos2x,tan2x and the quadrant of the angle 2x.      Log On


   

Question 1142719: if sinx=3/5 and x is an acute angle, use double angle formula to find the exact values of sin2x,cos2x,tan2x and the quadrant of the angle 2x.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if sinx=3/5 and x is an acute angle, use double angle formula to find the exact values of sin2x,cos2x,tan2x and the quadrant of the angle 2x.
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Step 1, find the cos(x)
Step 2, find the sin(2x) --- There's a formula for sin(2x) using sin(x) and cos(x).
If you don't know it, you can look it up.
I know it, there's no reason for me to look it up.
==================
Step 3, find the cos(2x)
Step 3, find the tan(2x)
=================
Angle 2x is in Q1
==========================

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We know that the sine of x is 3/5. We know that the sine is
opposite/hypotenuse. So we draw a right triangle with angle x
and put the numerator of 3/5, which is 3 on the side opposite
the angle x and put the denominator of 3/5, which is 5, on the
hypotenuse. We let the side adjacent to angle x be "a":

We calculate "a" by the Pythagorean theorem:
a%5E2%2Bb%5E2=c%5E2
a%5E2%2B3%5E2=5%5E2
a%5E2%2B9=25
a%5E2=16
sqrt%28a%5E2%29=sqrt%2816%29
a=4
So we put 4 on the adjacent side:

The rest is plugging in formulas, for we know that
sin%28x%29=3%2F5, cos%28x%29=4%2F5, tan%28x%29=3%2F4%29
Do you know the formulas? Do you know how to plug in?
If not, ask how in the note form below and I'll get back
to you by email.