# Some sort of trig question ???

• Sep 29th 2007, 09:54 PM
Burnt Flower
Some sort of trig question ???
Hi chaps, I got a Question here that has me confused , any thoughts or help is appreciated (how do we even use a calculator to find the answer?)
Thanks(Doh)

Given that cos
θ = -4/5 and π/2 ≤ θ ≤ π

find, in surd form (do not use calculators)

A) tan θ

B) Sin θ

C) sin (θ + 2π/3)

D) cos 2 θ
• Sep 29th 2007, 10:06 PM
Jhevon
Quote:

Originally Posted by Burnt Flower
Hi chaps, I got a Question here that has me confused , any thoughts or help is appreciated (how do we even use a calculator to find the answer?)
Thanks(Doh)

Given that cos
θ = -4/5 and π/2 ≤ θ ≤ π

find, in surd form (do not use calculators)

$\frac {\pi}2 \le \theta \le \pi$ means we are in the second quadrant. so we should know that only sine (and cosecant) is positive.

recall your trig ratios. $\mbox{cosine} = \frac {\mbox {Adjacent}}{\mbox {Hypotenuse}}$ etc.

knowing the cosine ratio, we can draw the right-triangle as you see below, with one acute angle $\theta$, with the adjacent side 4 and the hypotenuse 5. we can find the missing side by Pythagoras' theorem. now we can use the trig ratios to find the value of the other trig functions.

Quote:

A) tan θ
$\tan \theta = \frac {\mbox {Opposite}}{\mbox {Adjacent}}$

remember, the answer should be negative

Quote:

B) Sin θ
$\sin \theta = \frac {\mbox {Opposite}}{\mbox {Hypotenuse}}$

remember, the answer should be positive
Quote:

C) sin (θ + 2π/3)
use the addition formula for sine: $\sin (A + B) = \sin A \cos B + \sin B \cos A$

Quote:

D) cos 2 θ
use the double angle formula for cosine: $\cos 2 \theta = \cos^2 \theta - \sin^2 \theta$

EDIT: or you could use formulas. for instance, recall that: $\sin^2 \theta + \cos^2 \theta = 1$. you can use that to solve for sine if given cosine.