Question

Please help! Show the identities you use to evaluate the following. No calculators allowed!
a. sin 2α if cos α = 3/5 and 0 < α < π/2
b. cot(π/2 – x) if tan x = -5
c. cos(A + B) if cos A = 1/3 and cos B = 2/3
d. cos(-θ) if cos θ = -0.19
e. sin²(1.579) + cos²(1.579)
f. tan(x – y) if tan x = 5, tan y = 3, and x and y are in the first quadrant

Answer 1

e. =1 cause sin^2(a) + cos ^2(a) =1

Answer 2

c.cos(A+B)=cosacosb + sinasinb=1/3*2/3 + \[\sqrt{1- \cos^2(a)}\]\[\sqrt{1-\cos^2(b)}\]

Answer 3

f.tan(x-y) = tanx - tany/1+tanxtany = 1/8

Answer 4

e) They are squares of the functions of the same value. What does the pathagorean identity have to say about that?

Answer 5

Ah, doppler already covered that. hehe

Answer 6

is that really called pythagorean identity?even if ive heard that in college i got amnesia now:p

Answer 7

Ignore my poor typing skills and dyslexia. =P

Answer 8

no its ok lol when i saw your post i thought i missed some geometrical fact (connected that to pythagorean theorem) lol

Answer 9

a)
You know it is in the first quadrent. So make a simple triangle and fill in what you know!
That will let you find which is related to what and fill in the blanks pretty easily.

@doppler All you missed was its name. Hehe.