Thread: 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)

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.

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 ...

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

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

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

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?

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?

here's an idea ... use your calculator to check your work.

well i just wanted to know if I'm on the right track, and according to my calculator the answer is right, but i just wanted to know if that's the correct way.