# Values of Trig Functions

• May 25th 2008, 04:40 AM
Privatealpha
Values of Trig Functions
Hello, 1st post.
A little help needed.
We're not allowed to use calculators, so if you could provide answers with working, great!

Sinθ = - 2/5 (negative two fifths) Range: π ≤ θ ≤ 3π/2 (π=pi)

Find Values for:
Cosθ
Tanθ

Im told i am to use the triangles, but i dont get how they work.
Help is appreciated.
• May 25th 2008, 05:02 AM
TheEmptySet
Quote:

Originally Posted by Privatealpha
Hello, 1st post.
A little help needed.
We're not allowed to use calculators, so if you could provide answers with working, great!

Sinθ = - 2/5 (negative two fifths) Range: π ≤ θ ≤ 3π/2 (π=pi)

Find Values for:
Cosθ
Tanθ

Im told i am to use the triangles, but i dont get how they work.
Help is appreciated.

The sine function is negative in Quadrants III and IV

but we only want the Values in Quadrant III becuase of the range given.

Attachment 6493

Using the pythagorean theorem we can solve for the other leg of the triangle

$(-2)^2+x^2=5^2 \iff 4+x^2=25 \iff x=\sqrt{21}$

Note that since we are in quadrant III the x coordinate is negative.

so we get $-\sqrt{21}$

$\tan(\theta)=\frac{opposite}{adjacent}=\frac{-2}{-\sqrt{21}}=\frac{2\sqrt{21}}{21}$

$\cos(\theta)=\frac{adjacent}{hypotenuse}=\frac{-\sqrt{21}}{5}

$

I hope this helps.

Good luck.
• May 25th 2008, 06:18 AM
Privatealpha
Thanks for that.
Working through my assignment, it goes on to ask:
Evaluate Sin2 and Cos2 with the values above.

Ive come up with:
Sin2 = 2sin cos
=> 4√21 / 25

Cos2 = Cos² - Sin²
=> 1

Could someone confirm or correct my answers?
• May 25th 2008, 06:26 AM
Moo
Hello,

Quote:

Originally Posted by Privatealpha
Thanks for that.
Working through my assignment, it goes on to ask:
Evaluate Sin2 and Cos2 with the values above.

Ive come up with:
Sin2 = 2sin cos
=> 4√21 / 25

Cos2 = Cos² - Sin²
=> 1

Could someone confirm or correct my answers?

Ok for $\sin 2x$

$\cos 2x=\cos^2 x-\sin^2 x=\left(\frac{-\sqrt{21}}{5}\right)^2-\left(\frac{-2}{5}\right)^2=\frac{21}{25}-\frac{4}{25} \neq 1$

Also, you can remember the two other formulas for $\cos 2x$ : $2 \cos^2 x-1=1-2 \sin^2 x$

(Wink)