Thread: exact value of cos75, sin15, cot-210

ok so i need to find exact value of Cos75, Sin15 and Cot-210

for the first, i have the identity cos(a-b)=Cos(b)*Cos(a) + Sin(b)*Sin(a)

and im using 120 = a and 45 = b...cause i figured out cos and sin of those using the 30-60-90 and 45-45-90 triangle rules......but i have like: 1/root2 * -.5 + 1/root2 * root3 /2

and i dont know how to do this...i keep getting the wrong answer

so please help and help do the other two

thanks

Originally Posted by stones44

ok so i need to find exact value of Cos75, Sin15 and Cot-210

for the first, i have the identity cos(a-b)=Cos(b)*Cos(a) + Sin(b)*Sin(a)

and im using 120 = a and 45 = b...cause i figured out cos and sin of those using the 30-60-90 and 45-45-90 triangle rules......but i have like: 1/root2 * -.5 + 1/root2 * root3 /2

and i dont know how to do this...i keep getting the wrong answer

so please help and help do the other two

thanks

Your identity works just fine. Let a = 45 degrees and b = 30 degrees.
Then .

Originally Posted by stones44

ok so i need to find exact value of Cos75, Sin15 and Cot-210

for the first, i have the identity cos(a-b)=Cos(b)*Cos(a) + Sin(b)*Sin(a)

and im using 120 = a and 45 = b...cause i figured out cos and sin of those using the 30-60-90 and 45-45-90 triangle rules......but i have like: 1/root2 * -.5 + 1/root2 * root3 /2

and i dont know how to do this...i keep getting the wrong answer

so please help and help do the other two

thanks

You will probably want to use the identity for the computation of . And just so you're clear, .

Hello,

For the third one, you know that cot is an odd function.
Hence cot(-210)=-cot(210)

cot=cos/sin

Take 210=180+30

hmm ok..im having trouble with csc(-225)

can people not just give tips but do one out please..visuals help me

If one goes 225degrees clockwise it is the same as going 135degrees counter-clockwise from the positive x-axis.

well can you do one of them for me so i can get a feel for it? i get confused when there are multiple angles and stuff

mainly the csc one cause there arent identitys that ive learned that work with it

Originally Posted by stones44

the csc one cause there arent identitys that ive learned that work with it

That is an impossible for anyone who is doing a serious study of trigonometric functions.