Thread: how to find the exact value of sin,cos and tan of an angle?

1. how to find the exact value of sin,cos and tan of an angle?

find the exact values of the sine, cosine, and tangent of the angle.

11π/12 = 3π/4 + π/6

can you please explain how to do a question like this step by step.

thank you ( i was not in school when this was done so I'm not sure how or where to start)

2. Re: how to find the exact value of sin,cos and tan of an angle?

Originally Posted by Candy101
find the exact values of the sine, cosine, and tangent of the angle.

11π/12 = 3π/4 + π/6

can you please explain how to do a question like this step by step.

thank you ( i was not in school when this was done so I'm not sure how or where to start)

Go to this webpage.

3. Re: how to find the exact value of sin,cos and tan of an angle?

the two angles on the right side of the equation are unit circle angles ... you should already know the values for sine, cosine, and tangent for each of them.

plug and chug using the sum/difference identities ...

$\displaystyle \sin(a \pm b) = \sin(a)\cos(b) \pm \cos(a)\sin(b)$

$\displaystyle \cos(a \pm b) = \cos(a)\cos(b) \mp \sin(a)\sin(b)$

$\displaystyle \tan(a \pm b) = \frac{\tan(a) \pm \tan(b)}{1 \mp \tan(a)\tan(b)}$

4. Re: how to find the exact value of sin,cos and tan of an angle?

i try sin

$\displaystyle sin(3pi/4)Cos(pi/6)+cos(3pi/4)sin(Pi/6)$

and i got

√2/2 x √3/2 + -√2/2 x 1/2 = √6 - √2 /4 is this correct?

5. Re: how to find the exact value of sin,cos and tan of an angle?

Originally Posted by Candy101
i try sin

$\displaystyle sin(3pi/4)Cos(pi/6)+cos(3pi/4)sin(Pi/6)$

and i got

√2/2 x √3/2 + -√2/2 x 1/2 = √6 - √2 /4 is this correct?