# Give the exact value of the following (no calculators) :

• Apr 22nd 2013, 08:51 PM
boltage619
Give the exact value of the following (no calculators) :
cos (sin^-1 1/4 - tan^-1 (-3) )

Note: I posted a picture below with my work and i wanted to see if i'm correct, if not, please help me out, thanks!!! <3 (Nod)
• Apr 22nd 2013, 09:32 PM
spacemenon
Re: Give the exact value of the following (no calculators) :
cosx =1/sqrt15

cosy=1/sqrt 10

sinx=1/4

siny=-3/sqrt10

nw apply cos(x-y) ,u get 1/sqrt150 - 3/4sqrt10
• Apr 22nd 2013, 09:42 PM
boltage619
Re: Give the exact value of the following (no calculators) :
Thanks, can you help me out with my other post? =P
• Apr 22nd 2013, 09:48 PM
spacemenon
Re: Give the exact value of the following (no calculators) :
which one will try
• Apr 22nd 2013, 10:01 PM
boltage619
Re: Give the exact value of the following (no calculators) :
• Apr 23rd 2013, 04:19 PM
Soroban
Re: Give the exact value of the following (no calculators) :
Hello, boltage619!

Quote:

$\text{Solve over the interval }(0^o,\,360^o)\!: \;10\sin^2\theta - 13\sin\theta - 3 \:=\:0$

Factor: . $(2\sin\theta - 3)(5\sin\theta + 1) \:=\:0$

We have two equations to solve . . .

$2\sin\theta - 3 \:=\:0 \quad\Rightarrow\quad \sin\theta \:=\:\tfrac{3}{2} \quad\Rightarrow\quad \text{No real roots}$

$5\sin\theta + 1 \:=\:0 \quad\Rightarrow\quad \sin\theta \:=\:\text{-}\tfrac{1}{5} \quad\Rightarrow\quad \theta \:=\:\sin^{\text{-}1}\left(\text{-}\tfrac{1}{5}\right)$
. . $\theta \:=\:-11.53695903 \quad\Rightarrow\quad \theta \:=\:\begin{Bmatrix}191.5^o \\ 348.5^o\end{Bmatrix}$