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im supposed to use the special angle and a sum or difference identity but im not sure how to get started here.

1. sin 195 degrees

2. cos 285 degrees

please help..

2007-05-30 15:06:19 · 3 answers · asked by Alexis's Love Potion #9 4 in Science & Mathematics Mathematics

3 answers

Hopefully you've memorized the sine and cosine of the angles 30, 45, 60, 90, 120, 135, etc. That will make your life in Trig class a whole lot easier if you haven't :)

The secret is to look at 195 as 240 - 45.

That way,

sin(195)

= sin (240 - 45)

= sin 240 * cos 45 - cos 240 * sin 45

So, look at every "weird" angle as the sum or difference of familiar ones. Like 30 + 45 = 75 !!

Hope that helps ... :)

2007-05-30 15:16:39 · answer #1 · answered by Jeff 1 · 0 0

Since 195 = 180 + 15 = 180 + (45 - 30) then:

sin(195)
= sin(180)*cos(45 - 30) + cos(180)*sin(45 - 30)
= 0*cos(45 - 30) + -1*sin(45 - 30)
= -1*sin(45 - 30)
= -1[sin(45)*cos(30) - cos(45)*sin(45)]
= -1[(sqr rt(2)/2)*(sqr rt(3)/2) - (sqr rt(2)/2)*(1/2)]
= -1[sqr rt(6)/4 - sqr rt(2)/4]
= ( sqr rt(2) - sqr rt(6) )/4


To find the cos(285) do something similar. For example, 285 = 270 + 15 = 270 + (45 - 30). Or, 285 = 360 - 75 = 360 - (45 + 30).

2007-05-30 15:28:09 · answer #2 · answered by Jane D 1 · 0 0

(1) First, the sin (195) = - sin(75) and cos(285) = cos(75). This might give you a hint as where to go next [sin(a+b) = ? ]

2007-05-30 15:15:12 · answer #3 · answered by cattbarf 7 · 0 0

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