Question 1033133: I don't really understand the double-angle or the half-angle formula. Here are some problems I need to do:
1. If cos x = and x is a fourth-quadrant angle, evaluate sin 2x.
These are my answer choices:
*-sqrt(2)
*-1
*1
2. If θ is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate tan θ.
Answer choices:
*1/4
*1/2
*2/3
Please explain with lots of steps! Thanks.
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I don't really understand the double-angle or the half-angle formula. Here are some problems I need to do:
1. If cos t = sqrt(2)/2
and t is a fourth-quadrant angle, evaluate sin 2x.
cos = x/r, so x = sqrt(2), r = 2
----
Because t is in QIV y = -sqrt[2+4] = -sqrt(6)
So sin(t) = y/r = -sqrt(6)/2
---
Ans: sin(2t) = 2*sin(t)*cos(t) = 2[-sqrt(6)/2 *sqrt(2)/2] = -sqrt(12)/2
= -2sqrt(3)/2 = -sqrt(3)
======================================
2. If t is a first-quadrant angle in standard position with P(u, v) = (3, 4), evaluate tan t
Tan(t) = y/x = 4/3
=======================
Cheers,
Stan H.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! I don't really understand the double-angle or the half-angle formula. Here are some problems I need to do:
1. If cos x = and x is a fourth-quadrant angle, evaluate sin 2x.
---
No value is given for cos(x).
 -- that's Pythagoras, you have to know that.
--
There are sites that show the derivation of half-angles and double angles, but that's not usually necessary.
sin(2x) = 2*sin(x)*cos(x)
You can remember that, or look it up.
=========================================
These are my answer choices:
*-sqrt(2)
*-1
*1
===================================================
2. If theta is a first-quadrant angle in standard position with
P(u,v) = (3,4), evaluate tan(theta).
---
tan = y/x = 4/3
Not one of the choices.
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Answer choices:
*1/4
*1/2
*2/3
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