Using the identities to find the vales of each expression

[gator]

Ive been given very little notes from my teahcer, and can't do these. looked online, but its was no use.

1. Using the identities to find the vales of each expression (no calc.)
(i) sin t = 15/17 , cos t = 8/17 find remaining trig functions
(ii) sec^2 Pie/12 - tan^2 Pie/12

2. Find exact value
(i) tan* = -3 , cos *>0

3.Use reference angles to find exact value (no calc.)
(i) cos 225*
(ii) sin ( -pie/6 )


Thanks a bunch!

 

[TenaliRaman]

1.(i) Hint : 15^2 + 8^2 = 17^2
1.(ii) Hint : cos^2(x) = 1 - sin^2(x)
Divide throughout by [something] to get tan^2(x)

2.(i) ugly problem
use my hint for 1.(ii), you may not get exact angle though i am afraid

3.(i) Hint : 225 = 180 + 45
3.(ii) Hint : Think what about what i did in 3.(i)

-- AI

 

[verty]

Remember these three identities:

sin^2 + cos^2 = 1
sec^2 = 1 + tan^2
cosec^2 = 1 + cot^2

Learn them, be able to recite them.

One more thing, 2.(i) doesn't say 'no calc', so you can use your calculator there. What do the signs mean?

 

[mathman]

For (i), use definitions sec=1/cos, csc=1/sin, tan=sin/cos, cot=cos/sin.

 

[ryguy66]

I'm having trouble proving these trig identities:
1. sinB+cosBcotB = cscB
2. (sinA/1-cosA)-cotA = cscA
3. 2tan13X/1+tan^2 13X = sin26X
4. secX-tanX/cscX-1 = tanX

 

[HallsofIvy]

I'm having trouble proving these trig identities:
1. sinB+cosBcotB = cscB
2. (sinA/1-cosA)-cotA = cscA
3. 2tan13X/1+tan^2 13X = sin26X
4. secX-tanX/cscX-1 = tanX

1. PLEASE don't "hi-jack" someone else's thread for a completely different question- start your own thread.

2. "Having trouble" implies that you have made an effort. What have you done on these? Have tried converting everything to sine and cosine?

3. Be careful of your prentheses. A lot of people would interpret "secX-tanX/cscX- 1 as "secX- (tanX/cscX)- 1" but I suspect you mean
"(secX- tanX)/(cscX-1)".