What is sin(4a) & cos(4a) if tan(a)=3

Step-by-step explanation:

Your calculator can tell you these values:

  sin(4a) = sin(4·arctan(3)) = -0.96 = -24/25

  cos(4a) = cos(4·arctan(3)) = 0.28 = 7/25

Some useful trig identities are ...

  sin(2a) = 2tan(a)/(1 +tan(a)^2)

  cos(2a) = (1 -tan(a)^2)/(1 +tan(a)^2)

Filling in the given value for tan(a), we find ...

  sin(2a) = 2(3)/(1+3^2) = 6/10 = 3/5

  cos(2a) = (1 -3^2)/(1 +3^2) = -8/10 = -4/5

Now, double-angle formulas are useful:

  sin(4a) = 2sin(2a)cos(2a) = 2(3/5)(-4/5) = -24/25

  cos(4a) = 1 -2sin(2a)^2 = 1 -2(3/5)^2 = 7/25

The desired trig function values are sin(4a) = -24/25; cos(4a) = 7/25.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!