Unit Circle Trig

• Mar 4th 2009, 04:22 PM
realintegerz
Unit Circle Trig
I need a little helping hand on these 2 problems

1. Without using a calculator, find all solutions for t for 1 - 2 sin^2 t = 0 where t is in between or equal to 0 and 2pi

*So I got that sin t was equal to 1 / sq. root 2, but I'm not seeing how it matches up to one of the values of the unit circle...

2. Suppose alpha and beta are central angles in the unit circle (of radius 1) with initial sides on the positive x-axis. Further suppose that alpha is in quadrant 1 and beta is in quadrant 4 such that sine of alpha is 2/3 and cosine of beta is 1/4

a) Find the exact value of cosine alpha
b) Find the exact value of sine beta

*I have no clue on how to solve these.... (Headbang)
• Mar 4th 2009, 04:30 PM
skeeter
Quote:

Originally Posted by realintegerz
I need a little helping hand on these 2 problems

1. Without using a calculator, find all solutions for t for 1 - 2 sin^2 t = 0 where t is in between or equal to 0 and 2pi

*So I got that sin t was equal to 1 / sq. root 2, but I'm not seeing how it matches up to one of the values of the unit circle...

$\displaystyle \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$

look familiar now?

Quote:

2. Suppose alpha and beta are central angles in the unit circle (of radius 1) with initial sides on the positive x-axis. Further suppose that alpha is in quadrant 1 and beta is in quadrant 4 such that sine of alpha is 2/3 and cosine of beta is 1/4

a) Find the exact value of cosine alpha
b) Find the exact value of sine beta

from the unit circle, it should be clear to you that for any angle $\displaystyle \theta$,
$\displaystyle \sin^2{\theta} + \cos^2{\theta} = 1$

$\displaystyle \cos{\alpha} = \sqrt{1 - \sin^2{\alpha}}$

$\displaystyle \sin{\beta} = -\sqrt{1 - \cos^2{\beta}}$